NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers 2 — Questions and Answers
Question 1: In triangle ABC, angle A = 35° and angle B = 85°. What is the size of angle C?
- 55°
- 60° (Correct answer)
- 65°
- 70°
Correct answer: 60°
The sum of angles in a triangle = 180°. Angle C = 180° - 35° - 85° = 60°.
Question 2: A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
- 8 cm
- 10 cm
- 11 cm
- 12 cm (Correct answer)
Correct answer: 12 cm
Using Pythagoras: c² = a² + b². 13² = 5² + b². 169 = 25 + b². b² = 144. b = 12 cm.
Question 3: What is the area of a circle with radius 7 cm? (Use π ≈ 22/7)
- 154 cm² (Correct answer)
- 144 cm²
- 132 cm²
- 176 cm²
Correct answer: 154 cm²
Area = πr² = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 cm².
Question 4: If sin θ = 3/5, what is the value of cos θ for 0° < θ < 90°?
- 3/4
- 4/5 (Correct answer)
- 5/3
- 1/5
Correct answer: 4/5
Using sin²θ + cos²θ = 1: (3/5)² + cos²θ = 1. cos²θ = 1 - 9/25 = 16/25. cos θ = 4/5.
Question 5: A rectangle has length 12 cm and width 8 cm. What is the length of its diagonal?
- √(208) cm
- √(208) cm
- √(208) cm
- 4√(13) cm (Correct answer)
Correct answer: 4√(13) cm
Diagonal = √(12² + 8²) = √(144 + 64) = √208 = 4√13 cm.
Question 6: Two parallel lines are cut by a transversal. One co-interior (same-side interior) angle measures 65°. What does the other co-interior angle measure?
- 65°
- 115° (Correct answer)
- 125°
- 180°
Correct answer: 115°
Co-interior angles (also called consecutive interior angles) between parallel lines are supplementary — they add up to 180°. So the other angle = 180° - 65° = 115°.
NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers 2
In triangle ABC, angle A = 35° and angle B = 85°.
What is the size of angle C?