Step 1: Find the angle subtended by arc XY at the center O. The angle at the center is twice the angle at the circumference subtended by the same arc. Given ∠ XPY = 47°. ∠ XOY = 2 × ∠ XPY; ∠ XOY = 2 × 47° = 94° Step 2: Identify the angles formed by the tangents and radii. A radius drawn to the point of tangency is perpendicular to the tangent. Therefore, ∠ OXZ = 90° and ∠ OYZ = 90°. Step 3: Calculate ∠ XZY using the sum of angles in quadrilateral OXZY. The sum of interior angles in a quadrilateral is 360°. In quadrilateral OXZY: ∠ XOY + ∠ OXZ + ∠ OYZ + ∠ XZY = 360° Substitute the known angle values: 94° + 90° + 90° + ∠ XZY = 360°; 274° + ∠ XZY = 360°; ∠ XZY = 360° − 274°; ∠ XZY = 86° The final answer is B. 86°.

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Given XPY = 47^.

May 11, 2026Mathematics

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Answer

\text{B. } 86^\circ

Step-by-step solution

3 steps

Find the angle subtended by arc $XY$ at the center $O$ .
The angle at the center is twice the angle at the circumference subtended by the same arc.
Given $\angle XPY = 47^\circ$ .
$\angle XOY = 2 \times \angle XPY$ $\angle XOY = 2 \times 47^\circ = 94^\circ$
Identify the angles formed by the tangents and radii.
A radius drawn to the point of tangency is perpendicular to the tangent.
Therefore, $\angle OXZ = 90^\circ$ and $\angle OYZ = 90^\circ$ .
Calculate $\angle XZY$ using the sum of angles in quadrilateral $OXZY$ .
The sum of interior angles in a quadrilateral is $360^\circ$ .
In quadrilateral $OXZY$ :
$\angle XOY + \angle OXZ + \angle OYZ + \angle XZY = 360^\circ$
Substitute the known angle values:
$94^\circ + 90^\circ + 90^\circ + \angle XZY = 360^\circ$ $274^\circ + \angle XZY = 360^\circ$ $\angle XZY = 360^\circ - 274^\circ$ $\angle XZY = 86^\circ$
The final answer is $\text{B. } 86^\circ$ .

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Given XPY = 47^.

Answer

Step-by-step solution

Find the angle subtended by arc XYXYXY at the center OOO.

Identify the angles formed by the tangents and radii.

Calculate ∠XZY\angle XZY∠XZY using the sum of angles in quadrilateral OXZYOXZYOXZY.

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More Mathematics Questions

Find the angle subtended by arc $XY$ at the center $O$ .

Calculate $\angle XZY$ using the sum of angles in quadrilateral $OXZY$ .