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प्रश्न
In the given figure, O is centre of the circle and \[\angle \mathrm{B}=55^{\circ}\]. The angle A is equal to ______.
पर्याय
55°
35°
45°
50°
MCQ
रिकाम्या जागा भरा
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उत्तर
In the given figure, O is centre of the circle and \[\angle \mathrm{B}=55^{\circ}\]. The angle A is equal to 35°.
Explanation:
From figure,
In △ OCB,
OB = OC (Radius of common circle)
We know that,
Angles opposite to equal sides of a triangle are equal.
∴ ∠C = ∠B = 55°
By angle sum property of triangle,
⇒ ∠C + ∠B + ∠O = 180°
⇒ 55° + 55° + ∠O = 180°
⇒ ∠O + 110° = 180°
⇒ ∠O = 180° - 110° = 70°.
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∠A
⇒ ∠A = `(∠O)/2 = (70°)/2` = 35°
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