In the given figure, PQ is diamerter of

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

In the given figure, PQ is diamerter of the semicircle PABQ and O is its center. ∠AOB = 66°, BP cuts AQ at X. What is the value (in degrees) of ∠AXP?

Options:

56°

57°

58°

67°

Correct Answer:

57°

Explanation:

∠AOB = 66°

⇒ ∠BPA = $\frac{66}{2}=33°$ (angle by same chord)

⇒ ∠PAQ = 90° (PQ is a diameter)

So, ∠

PXA = 90° - 33° = 57°