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प्रश्न
In the given figure, O is centre of the circle and angle OBA = 50°.
The angle P is ______.
पर्याय
50°
80°
40°
60°
MCQ
रिकाम्या जागा भरा
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उत्तर
In the given figure, O is centre of the circle and angle OBA = 50°.
The angle P is 40°.
Explanation:
From figure,
In △ OAB,
OA = OB (Radius of common circle)
We know that,
Angles opposite to equal sides of a triangle are equal.
∴ ∠A = ∠B = 50°
By angle sum property of triangle,
⇒ ∠A + ∠B + ∠O = 180°
⇒ 50° + 50° + ∠O = 180°
⇒ ∠O + 100° = 180°
⇒ ∠O = 180° - 100° = 80°.
We know that,
The angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference.
⇒ ∠O = 2∠P
⇒ ∠P = `(∠O)/2` = `(80°)/2`= 40°.
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