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Question
In the above figure, if ∠P = 50°, then reflex angle AOB is ______.
Options
2 × 50°
180° − 60°
230°
none of these
MCQ
Fill in the Blanks
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Solution
In the above figure, if ∠P = 50°, then reflex angle AOB is 230°.
Explanation:
Join OB.
We know that,
Tangent at any point of a circle and the radius through this point are perpendicular to each other.
∴ ∠OAP = 90° and ∠OBP = 90°
In quadrilateral OAPB,
⇒ ∠OAP + ∠APB + ∠PBO + ∠AOB = 360°
⇒ 90° + 50° + 90° + ∠AOB = 360°
⇒ ∠AOB + 230° = 360°
⇒ ∠AOB = 360° − 230° = 130°
Reflex ∠AOB = 360° − ∠AOB = 360° − 130° = 230°
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