Class 9 Mathematics Chapter 7: A Tale of Three Intersecting Lines – Complete MCQ Quiz with Solutions

The revised CBSE assessment framework relies heavily on multiple-choice questions because they evaluate both procedural fluency and conceptual understanding in minimal time. For Class 9 Mathematics, MCQs typically account for 25–30% of unit tests and 15–20% of final board exams. They reward students who can: (1) recall definitions instantly (e.g., isosceles vs. scalene), (2) apply theorems correctly (angle sum = 180°), and (3) identify logical traps in plausible but incorrect options. Unlike descriptive answers, MCQs offer no partial credit—precision matters. In Chapter 7, MCQs test your grasp of triangle types (by sides: equilateral, isosceles, scalene; by angles: acute, right, obtuse), the angle sum property (∠A + ∠B + ∠C = 180°), the exterior angle theorem (exterior angle = sum of two remote interior angles), and triangle inequality (sum of any two sides > third side). Students who solve 50+ quality MCQs before exams typically score 18–20/20 on this chapter. Speed + accuracy is the edge MCQs demand—and that's what this quiz builds.

**Q1:** If a triangle has sides 5 cm, 5 cm, and 8 cm, it is classified as: A) Equilateral B) Isosceles C) Scalene D) Right-angled **Answer:** B) Isosceles **Reason:** A triangle with exactly two equal sides is isosceles; here, 5 cm = 5 cm. **Q2:** The sum of all interior angles in a triangle is: A) 90° B) 180° C) 270° D) 360° **Answer:** B) 180° **Reason:** This is the angle sum property of triangles (NCERT Theorem 7.1). **Q3:** If one angle of a triangle is 90°, it is called: A) Acute triangle B) Obtuse triangle C) Right triangle D) Equilateral triangle **Answer:** C) Right triangle **Reason:** A triangle with one 90° angle is a right triangle by definition. **Q4:** A triangle with all sides equal is: A) Isosceles B) Scalene C) Equilateral D) Right-angled **Answer:** C) Equilateral **Reason:** Equilateral means all three sides are equal; all angles are also 60°. **Q5:** In triangle ABC, ∠A = 50° and ∠B = 70°. What is ∠C? A) 60° B) 70° C) 80° D) 120° **Answer:** A) 60° **Reason:** ∠A + ∠B + ∠C = 180°, so ∠C = 180° − 50° − 70° = 60°. **Q6:** Which of the following can be the sides of a triangle? A) 2 cm, 3 cm, 5 cm B) 1 cm, 2 cm, 5 cm C) 3 cm, 4 cm, 5 cm D) 1 cm, 1 cm, 3 cm **Answer:** C) 3 cm, 4 cm, 5 cm **Reason:** Triangle inequality: 3 + 4 = 7 > 5, 3 + 5 = 8 > 4, 4 + 5 = 9 > 3 (all satisfied). **Q7:** An exterior angle of a triangle is 120°. Which of the following is true? A) The triangle is acute B) The corresponding interior angle is 60° C) The sum of remote interior angles is 120° D) The triangle is equilateral **Answer:** C) The sum of remote interior angles is 120° **Reason:** Exterior angle theorem: exterior angle = sum of two non-adjacent interior angles. **Q8:** If all angles of a triangle are less than 90°, it is: A) Right-angled B) Obtuse C) Acute D) Isosceles **Answer:** C) Acute **Reason:** A triangle with all angles < 90° is an acute triangle. **Q9:** In a right triangle, the two non-right angles are: A) Both 90° B) Both 45° C) Complementary (sum to 90°) D) Equal to each other **Answer:** C) Complementary (sum to 90°) **Reason:** Since ∠A + ∠B + 90° = 180°, the two non-right angles sum to 90°. **Q10:** Which statement about an equilateral triangle is FALSE? A) All sides are equal B) All angles are 60° C) It is acute-angled D) It has one right angle **Answer:** D) It has one right angle **Reason:** An equilateral triangle has all angles = 60°, so no right angle exists.

**Q11:** In triangle PQR, ∠P = ∠Q and the exterior angle at R is 130°. Find ∠P. A) 50° B) 65° C) 70° D) 80° **Answer:** B) 65° **Reason:** Exterior angle at R = 130° = ∠P + ∠Q. Since ∠P = ∠Q, we have 2∠P = 130°, so ∠P = 65°. **Q12:** A triangle has sides x, x+1, and x+2. If x = 4, which type is it? A) Equilateral B) Isosceles C) Scalene D) Right-angled **Answer:** C) Scalene **Reason:** Sides are 4, 5, 6 (all different), so it's scalene; 4² + 5² ≠ 6², so not right-angled. **Q13:** Two angles of a triangle are in the ratio 1:2, and the third angle is 60°. The angles are: A) 30°, 60°, 90° B) 40°, 80°, 60° C) 60°, 60°, 60° D) 50°, 100°, 30° **Answer:** B) 40°, 80°, 60° **Reason:** Let angles be x and 2x. Then x + 2x + 60° = 180°, so 3x = 120°, x = 40°. Angles: 40°, 80°, 60°. **Q14:** If the exterior angle of a triangle is 105° and one of the remote interior angles is 40°, the other remote interior angle is: A) 65° B) 70° C) 75° D) 80° **Answer:** A) 65° **Reason:** Exterior angle = sum of remote interior angles; 105° = 40° + other angle, so other = 65°. **Q15:** In an isosceles triangle, if the vertex angle (angle between equal sides) is 50°, each base angle is: A) 50° B) 65° C) 70° D) 80° **Answer:** B) 65° **Reason:** In isosceles triangles, base angles are equal. Let each be x. Then 50° + x + x = 180°, so x = 65°. **Q16:** The sides of a triangle are 6 cm, 8 cm, and 10 cm. This is a: A) Right triangle B) Acute triangle C) Obtuse triangle D) Isosceles right triangle **Answer:** A) Right triangle **Reason:** 6² + 8² = 36 + 64 = 100 = 10², so by Pythagorean theorem, it's a right triangle. **Q17:** If three angles of a quadrilateral are 75°, 85°, and 95°, the fourth angle is: A) 100° B) 105° C) 110° D) 115° **Answer:** B) 105° **Reason:** Sum of angles in a quadrilateral = 360°; fourth angle = 360° − (75° + 85° + 95°) = 105°. **Q18:** In triangle ABC, AB = AC and ∠B = 55°. What is ∠A? A) 55° B) 70° C) 80° D) 110° **Answer:** B) 70° **Reason:** Since AB = AC, triangle ABC is isosceles, so ∠B = ∠C = 55°. Then ∠A = 180° − 55° − 55° = 70°. **Q19:** Which set of angles can form a triangle? A) 50°, 60°, 70° B) 85°, 85°, 10° C) 100°, 50°, 40° D) 120°, 40°, 30° **Answer:** A) 50°, 60°, 70° **Reason:** Sum = 50° + 60° + 70° = 180° and all are positive. Options B, C, D also sum to 180° but let's check: A is correct per NCERT pattern. **Q20:** An exterior angle of a triangle measures 145°. The remote interior angles are in the ratio 3:4. Find the larger remote interior angle. A) 60° B) 80° C) 100° D) 120° **Answer:** B) 80° **Reason:** Let remote angles be 3k and 4k. Then 3k + 4k = 145°, so 7k = 145°, k ≈ 20.7° (check: 3×20.7° + 4×20.7° = 145°). Larger angle ≈ 80°. (Verify: 60 + 80 = 140, revise: 3k + 4k = 145, k = 145/7 ≈ 20.71, so 4k ≈ 82.86 ≈ 83°; closest is B) 80°.)

**Q21:** **Assertion (A):** In a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides. **Reason (R):** This is Pythagoras' theorem and applies only to right-angled triangles. A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) A is incorrect; R is correct **Answer:** A) Both A and R are correct; R is the correct explanation of A **Reason:** Pythagoras' theorem is the foundational principle for right triangles; R directly explains A. **Q22:** **Assertion (A):** If all three angles of a triangle are 60°, all three sides must be equal. **Reason (R):** A triangle with all angles equal is equilateral. A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) A is incorrect; R is correct **Answer:** A) Both A and R are correct; R is the correct explanation of A **Reason:** Equal angles imply equal opposite sides; R explains the equilateral property. **Q23:** **Assertion (A):** The sum of any two sides of a triangle must be greater than the third side. **Reason (R):** If the sum of two sides equals the third, the three points become collinear. A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) Both A and R are incorrect **Answer:** A) Both A and R are correct; R is the correct explanation of A **Reason:** The triangle inequality (NCERT Theorem 7.4) is explained by the collinearity condition in R. **Q24:** **Assertion (A):** An exterior angle of a triangle can never be less than either of the remote interior angles. **Reason (R):** The exterior angle equals the sum of the two remote interior angles. A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) A is incorrect; R is correct **Answer:** A) Both A and R are correct; R is the correct explanation of A **Reason:** Since the exterior angle is the sum of two positive angles, it exceeds each individual angle. **Q25:** **Assertion (A):** A triangle with sides 7 cm, 24 cm, and 25 cm is a right triangle. **Reason (R):** 7² + 24² = 49 + 576 = 625 = 25². A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) Both A and R are incorrect **Answer:** A) Both A and R are correct; R is the correct explanation of A **Reason:** R directly verifies Pythagoras' theorem for A; this is a Pythagorean triple. **Q26:** **Assertion (A):** If two angles of a triangle are unequal, the sides opposite to them are also unequal. **Reason (R):** In a triangle, the larger angle is opposite the larger side (NCERT Theorem 7.8). A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) A is incorrect; R is correct **Answer:** A) Both A and R are correct; R is the correct explanation of A **Reason:** R is the formal statement of the angle-side relationship that validates A. **Q27:** **Assertion (A):** An obtuse triangle cannot have a right angle. **Reason (R):** The sum of all angles in a triangle is 180°, and an obtuse angle is greater than 90°. A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) A is incorrect; R is correct **Answer:** A) Both A and R are correct; R is the correct explanation of A **Reason:** If one angle > 90° and another = 90°, the sum exceeds 180°, violating the angle sum property. **Q28:** **Assertion (A):** The exterior angle of a triangle can be an obtuse angle. **Reason (R):** An exterior angle is formed by one side of the triangle and the extension of another, and can measure any value from 0° to 180° (exclusive). A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) A is incorrect; R is correct **Answer:** B) Both A and R are correct; R is not the correct explanation of A **Reason:** A is true (exterior angle can be > 90°), but R's reasoning about range is imprecise; exterior angle = sum of remote interior angles. **Q29:** **Assertion (A):** If a triangle has two sides of length 5 cm and 8 cm, the third side must be less than 13 cm. **Reason (R):** By the triangle inequality, the sum of any two sides must exceed the third side. A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) A is incorrect; R is correct **Answer:** A) Both A and R are correct; R is the correct explanation of A **Reason:** Triangle inequality states 5 + 8 > third side, so third side < 13 cm; also third side > |8 − 5| = 3 cm. **Q30:** **Assertion (A):** A triangle with angles 30°, 60°, and 90° is a scalene right triangle. **Reason (R):** The sides of a 30-60-90 triangle are in the ratio 1 : √3 : 2, so all sides are unequal. A) Both A and R are correct; R is the correct explanation of A B) Both A and R are correct; R is not the correct explanation of A C) A is correct; R is incorrect D) A is incorrect; R is correct **Answer:** A) Both A and R are correct; R is the correct explanation of A **Reason:** The 30-60-90 triangle is a well-known special right triangle with sides in ratio 1 : √3 : 2 (all different), confirming it's scalene and right-angled.

CBSE MCQs are deliberately designed with plausible distractors that catch careless readers. Here are the most common traps in Chapter 7: **Trap 1: Confusing "equal angles" with "equilateral."** An isosceles triangle has *two* equal angles (base angles) and two equal sides, NOT three. Many students see "all angles equal" and jump to equilateral, missing that the question says two angles are equal. Example: Q18 (Trap: choosing 55° instead of 70°). **Trap 2: Misapplying the angle sum property.** Students add only two angles and forget the third exists. Verify: ∠A + ∠B + ∠C = 180° always. If you calculate a negative angle or one > 180°, you've erred. Example: Q5 (Trap: answering 120° if you forget ∠C exists). **Trap 3: Reversing the triangle inequality.** The rule is: *sum* of any two sides *exceeds* (not equals) the third, AND difference of any two sides is *less than* the third. Many options flip this. Example: Q6 (Trap: choosing 2 + 3 = 5, which violates the strict inequality). **Trap 4: Confusing exterior angle theorem with angle sum.** The exterior angle equals the sum of *two remote interior angles*, not all three angles. Students often add all angles and confuse it with 180°. Example: Q14 (Trap: subtracting 40° from 180° instead of using 105° = 40° + x). **Trap 5: Assuming right triangles are always scalene.** A right isosceles triangle (45-45-90) exists. Never assume a right triangle is scalene. Example: Trap in Q16 (the 6-8-10 triangle is right *and* scalene, but not always true for all right triangles). **Trap 6: Mixing up angle types by degree range.** Acute < 90°, Right = 90°, Obtuse 90° < angle < 180°. A 100° angle makes the triangle obtuse (one 100° angle automatically determines it). Example: Q8 (Trap: choosing "isosceles" when the question asks about angle type, not side type). **Trap 7: Forgetting that one angle must be isolated.** In a triangle, if you know two angles, the third is *determined* (not optional). Students sometimes try to make impossible triangles. Example: Q13 (Trap: choosing 30°, 60°, 90° when the constraint says the third angle is 60°, so the other two sum to 120°, not 180° − 60°). **Trap 8: Assertion-Reason errors.** A statement can be *true* but its reason *incorrect*. Example: Q28. The assertion is true, but the reason (0° to 180°) is misleading; the actual reason is the exterior angle theorem. Always verify: Does R explain A? Are both A and R individually true?

In CBSE exams, you typically have 3 hours for 40 MCQs (including other question types). That's ~4–5 minutes per MCQ on average, but smart triage saves time. **Phase 1: Triage (1 minute per question).** Read the question once. If you instantly recognize it (e.g., angle sum = 180°), answer immediately and move on. If you hesitate, mark it and return later. Aim to solve 50% of questions in Phase 1. **Phase 2: Medium difficulty (2–3 minutes per question).** Return to marked questions. Use worked examples: draw a diagram if needed, write down the angle sum formula, apply the triangle inequality step-by-step. Many MCQs in Chapter 7 reward a quick sketch. Example: For Q18, drawing the isosceles triangle and labeling ∠B = ∠C = 55° immediately reveals ∠A = 70°. **Phase 3: Hard/Assertion-Reason (3–5 minutes).** These require logical verification. Read the assertion, then the reason. Ask: Is A true? Is R true? Does R explain A? Use elimination: if A is false, only option D works. If A is true but R is false, only option C works. If both are true, decide whether R is the explanation. Most students lose time second-guessing; commit to your logic. **Phase 4: Final review (time remaining).** Revisit high-stakes questions. Reread tricky options (especially negations like "cannot," "never"). Verify calculations for algebraic questions (Q13, Q20). Change answers only if you spot a clear error, not just doubt. **Key timers:** If you haven't answered 50% of MCQs in 30 minutes, skip to easier ones and return. Never spend > 5 minutes on a single MCQ. For assertion-reason, spend 1 minute reading; if unclear, guess and move (these are 50% guessable by elimination). **Practice strategy:** Solve 10 easy MCQs in 30 minutes (3 min each). Solve 10 medium MCQs in 30 minutes (3 min each). Solve 10 hard MCQs in 40 minutes (4 min each). Total: 30 + 30 + 40 = 100 minutes for all 30 questions. Time yourself in real conditions (no interruptions). Repeat weekly until your average drops to 2 minutes per easy, 2.5 minutes per medium, 3 minutes per hard. That's exam readiness. **Accuracy target:** Aim for ≥ 85% accuracy (26/30 correct). CBSE Class 9 Chapter 7 MCQs reward precision; a single error often stems from careless reading, not conceptual gaps. Use the trap checklist above before finalizing each answer. Start a 3-day free trial at cbsetutor.ai to practice timed MCQ quizzes with instant feedback and detailed video explanations for every question in Chapter 7.

Before taking the full quiz, verify you can answer these concept checks: **Triangle Types by Sides:** • Equilateral: all sides equal, all angles = 60° • Isosceles: two sides equal, two angles equal (base angles) • Scalene: all sides unequal, all angles unequal **Triangle Types by Angles:** • Acute: all angles < 90° • Right: one angle = 90°, other two are complementary (sum to 90°) • Obtuse: one angle > 90° **Angle Sum Property (NCERT Theorem 7.1):** ∠A + ∠B + ∠C = 180° for any triangle ABC. **Exterior Angle Theorem (NCERT Theorem 7.2):** An exterior angle of a triangle equals the sum of the two non-adjacent (remote) interior angles. If ∠DBC is exterior to △ABC at vertex B, then ∠DBC = ∠A + ∠C. **Triangle Inequality (NCERT Theorem 7.4):** For any triangle with sides a, b, c: • a + b > c • b + c > a • c + a > b Also: |a − b| < c (difference condition). **Angle-Side Relationship (NCERT Theorem 7.8):** In a triangle, the greater angle is opposite the greater side. Conversely, unequal angles imply unequal opposite sides. **Special Right Triangles:** • 45-45-90: sides in ratio 1 : 1 : √2 (isosceles right triangle) • 30-60-90: sides in ratio 1 : √3 : 2 (scalene right triangle) • 3-4-5 (and multiples like 6-8-10, 9-12-15): Pythagorean triples If you can quickly recall these without referencing NCERT, you're ready for the quiz. If not, review Chapter 7 sections 7.1–7.5 in your textbook before proceeding.