In the given figure, AP is perpendicular

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Home Questions 7RBJKFACCZ

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

In the given figure, AP is perpendicular to BC and AQ is bisector of angle PAC. What will be the measure of angle PQA?

Options:

25°

45°

55°

65°

Correct Answer:

65°

Explanation:

In triangle APC

∠P = 90°, ∠C = 40°

So, ∠PAC = 180° - (90° + 40°) = 50°

∠PAQ = \(\frac{1}{2}\) ∠PAC = \(\frac{50°}{2}\) = 25°

In triangle APQ

⇒ ∠Q = 180° - (∠P + ∠A) = 180° - (90° + 25°) = 65°