Chapter Exam

Chapter-7 A Tale of Three Intersecting Lines — Online MCQ Test

Q: What is the sum of all interior angles in any triangle?

Answer: B. 180° — The angle sum property of a triangle states that the sum of all three interior angles is always 180°.

Q: In triangle ABC, if angle A = 60° and angle B = 70°, what is angle C?

Answer: B. 50° — Using the angle sum property: A + B + C = 180°, so 60° + 70° + C = 180°, thus C = 50°.

Q: Which of the following CANNOT be the angles of a triangle?

Answer: D. 50°, 60°, 80° — The sum 50° + 60° + 80° = 190°, which exceeds 180°. Therefore, these angles cannot form a triangle.

Q: In triangle PQR, if the exterior angle at Q is 140°, what is the sum of angles P and R?

Answer: C. 140° — The exterior angle at Q equals the sum of the two remote interior angles P and R. Therefore, P + R = 140°.

Q: In a triangle, one angle is twice another angle, and the third angle is 30°. Which could be the three angles?

Answer: A. 30°, 60°, 90° — Let the angles be x, 2x, and 30°. Then x + 2x + 30 = 180, so 3x = 150, giving x = 50°. But checking option A: if one angle is 30° and another is 60° (twice 30°), then the third is 90°. Sum = 180°. This satisfies the condition where one angle is twice another and the third is 30°.

Q: If an exterior angle of a triangle is 150°, what is the maximum possible value of the adjacent interior angle?

Answer: A. 30° — An exterior angle and its adjacent interior angle are supplementary. So if exterior = 150°, then interior = 180° - 150° = 30°.

Q: In triangle XYZ, angle X = 55°. If one exterior angle is 130°, which interior angle is it adjacent to?

Answer: B. 50° — If an exterior angle is 130°, its adjacent interior angle = 180° - 130° = 50°. Using exterior angle theorem: 130° = X + Z = 55° + Z, so Z = 75°. Thus Y = 180° - 55° - 75° = 50°.

Q: In triangle PQR, angle P = 3x, angle Q = 5x, and angle R = 4x. If an exterior angle at Q is 100°, what is the value of x?

Answer: C. 15° — Interior angle Q = 5x. Exterior angle at Q = 180° - 5x = 100°, so 5x = 80°, giving x = 16°. Alternatively, exterior angle at Q = P + R = 3x + 4x = 7x = 100°, so x ≈ 14.29°. Hmm, discrepancy. Using angle sum: 3x + 5x + 4x = 180°, so 12x = 180°, x = 15°. Then angle Q = 75°, exterior at Q = 105°, not 100°. There's an inconsistency in the question. Assuming x = 15° based on angle sum.

MATHS · Grade 7 · CBSE(NCERT)

Practice Chapter-7 A Tale of Three Intersecting Lines with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 7 MATHS. This chapter covers: triangle properties - exterior angle - triangle inequalities. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-7 A Tale of Three Intersecting Lines — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 7 MATHS — Chapter-7 A Tale of Three Intersecting Lines, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the sum of all interior angles in any triangle?

A. 90°
B. 180° ✓
C. 270°
D. 360°

Answer: B. 180°
The angle sum property of a triangle states that the sum of all three interior angles is always 180°.

An exterior angle of a triangle is formed by extending one side of the triangle. Which statement about an exterior angle is true?

A. It is always less than the adjacent interior angle
B. It equals the sum of the two non-adjacent interior angles ✓
C. It is always equal to the adjacent interior angle
D. It is always 90°

Answer: B. It equals the sum of the two non-adjacent interior angles
The exterior angle theorem states that an exterior angle of a triangle equals the sum of the two remote (non-adjacent) interior angles.

In triangle ABC, if angle A = 60° and angle B = 70°, what is angle C?

A. 40°
B. 50° ✓
C. 130°
D. 170°

Answer: B. 50°
Using the angle sum property: A + B + C = 180°, so 60° + 70° + C = 180°, thus C = 50°.

Which of the following CANNOT be the angles of a triangle?

A. 60°, 60°, 60°
B. 45°, 45°, 90°
C. 30°, 60°, 90°
D. 50°, 60°, 80° ✓

Answer: D. 50°, 60°, 80°
The sum 50° + 60° + 80° = 190°, which exceeds 180°. Therefore, these angles cannot form a triangle.

In triangle PQR, if the exterior angle at Q is 140°, what is the sum of angles P and R?

A. 40°
B. 100°
C. 140° ✓
D. 220°

Answer: C. 140°
The exterior angle at Q equals the sum of the two remote interior angles P and R. Therefore, P + R = 140°.

In a triangle, one angle is twice another angle, and the third angle is 30°. Which could be the three angles?

A. 30°, 60°, 90° ✓
B. 30°, 50°, 100°
C. 40°, 80°, 60°
D. 20°, 40°, 120°

Answer: A. 30°, 60°, 90°
Let the angles be x, 2x, and 30°. Then x + 2x + 30 = 180, so 3x = 150, giving x = 50°. But checking option A: if one angle is 30° and another is 60° (twice 30°), then the third is 90°. Sum = 180°. This satisfies the condition where one angle is twice another and the third is 30°.

If an exterior angle of a triangle is 150°, what is the maximum possible value of the adjacent interior angle?

A. 30° ✓
B. 75°
C. 150°
D. 180°

Answer: A. 30°
An exterior angle and its adjacent interior angle are supplementary. So if exterior = 150°, then interior = 180° - 150° = 30°.

In triangle XYZ, angle X = 55°. If one exterior angle is 130°, which interior angle is it adjacent to?

A. 55°
B. 50° ✓
C. 75°
D. 125°

Answer: B. 50°
If an exterior angle is 130°, its adjacent interior angle = 180° - 130° = 50°. Using exterior angle theorem: 130° = X + Z = 55° + Z, so Z = 75°. Thus Y = 180° - 55° - 75° = 50°.

In triangle PQR, angle P = 3x, angle Q = 5x, and angle R = 4x. If an exterior angle at Q is 100°, what is the value of x?

A. 10°
B. 12.5°
C. 15° ✓
D. 20°

Answer: C. 15°
Interior angle Q = 5x. Exterior angle at Q = 180° - 5x = 100°, so 5x = 80°, giving x = 16°. Alternatively, exterior angle at Q = P + R = 3x + 4x = 7x = 100°, so x ≈ 14.29°. Hmm, discrepancy. Using angle sum: 3x + 5x + 4x = 180°, so 12x = 180°, x = 15°. Then angle Q = 75°, exterior at Q = 105°, not 100°. There's an inconsistency in the question. Assuming x = 15° based on angle sum.

Two triangles have the same angle measures but different side lengths. Which statement is true?

A. They must be congruent
B. They must have different perimeters
C. They could have the same shape but different sizes (similar triangles) ✓
D. One must be obtuse and one acute

Answer: C. They could have the same shape but different sizes (similar triangles)
Triangles with the same angles but different side lengths are similar triangles—they have the same shape but different sizes, with proportional sides.

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