In the adjoining figure,O is the centre of circle.find the measure of angle BOC
Answers
Answer:
The measure of ∠BOC is 160° and ∠BDC is 80°.
Step-by-step explanation:
It is given that BA = AC, it means triangle ABC is an isosceles triangle. The two angles inclined on equal and non equal lines are same.
\angle ABC=\angle ACB=50^{\circ}∠ABC=∠ACB=50
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Using the angle sum property of triangle,
\angle ABC+\angle ACB+\angle BAC=180^{\circ}∠ABC+∠ACB+∠BAC=180
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50^{\circ}+50^{\circ}+\angle BAC=180^{\circ}50
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+50
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+∠BAC=180
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100^{\circ}+\angle BAC=180^{\circ}100
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+∠BAC=180
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\angle BAC=80^{\circ}∠BAC=80
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According to the central angle theorem, the central angle from any two points on the circle is always twice the inscribed angle from those two points.
\angle BOC=2\times \angle BAC∠BOC=2×∠BAC
\angle BOC=2\times 80^{\circ}∠BOC=2×80
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\angle BOC=160^{\circ}∠BOC=160
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Using central angle theorem,
\angle BOC=2\times \angle BDC∠BOC=2×∠BDC
160^{\circ}=2\times \angle BDC160
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=2×∠BDC
\angle BDC=80^{\circ}∠BDC=80
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Therefore the measure of ∠BOC is 160° and ∠BDC is 80°.
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