"Question 1 In the given figure, A, B and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.
Class 9 - Math - Circles Page 184"
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This is your answer that is 45
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∠BOC = 30° and ∠AOB = 60° [Given]
∴∠AOC = ∠BOC + ∠AOB
= 30° + 60°
= 90°
∠ADC = 1/2 ∠AOC
{Angle on centre and angle on circumference from same sector rule}
∴∠ADC = 1/2 × 90°
= 45°
Therefore, ∠ADC = 45°
I hope it helps you ^_^
∴∠AOC = ∠BOC + ∠AOB
= 30° + 60°
= 90°
∠ADC = 1/2 ∠AOC
{Angle on centre and angle on circumference from same sector rule}
∴∠ADC = 1/2 × 90°
= 45°
Therefore, ∠ADC = 45°
I hope it helps you ^_^
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