In the given figure- O is the center of the incircle of ABC- If - BAC - 65- and - BCA - 75- then find - ROQ-

The correct option is C 140° In triangle ABC ∠ A + ∠ B + ∠ C = 180^∘ 65^∘ + ∠ B + 75^∘ = 180^∘ ∠ B = 40^∘ We know that ∠ ORB = 90^∘ and ∠ OQB = 90^∘ ∠ ROQ = ...

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Byju's Answer

Standard X

Mathematics

Basic Properties of a Circle

In the given ...

Question

In the given figure, O is the center of the incircle of $△$ ABC. If $∠ B A C$ = $65^{\circ}$ and $∠ B C A$ = $75^{\circ}$ , then find $∠ R O Q$ .

80°

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120°

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140°

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Solution

The correct option is C
140°

In triangle ABC

$∠ A + ∠ B + ∠ C = 180^{\circ}$

$65^{\circ} + ∠ B + 75^{\circ} = 180^{\circ}$

$∠ B = 40^{\circ}$

We know that $∠ O R B = 90^{\circ}$ and $∠ O Q B = 90^{\circ}$

$∠ R O Q = 180^{\circ} - ∠ B$

$∠ R O Q = 180^{\circ} - 40^{\circ} = 140^{\circ}$

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In the given figure, O is the center of the incircle of △ABC. If ∠BAC = 65∘ and ∠BCA = 75∘, then find ∠ROQ.

The correct option is C 140° In triangle ABC ∠A+∠B+∠C=180∘ 65∘+∠B+75∘=180∘ ∠B=40∘ We know that ∠ORB=90∘ and ∠OQB=90∘ ∠ROQ=180∘−∠B ∠ROQ=180∘–40∘=140∘

In the given figure, O is the center of the incircle of $△$ ABC. If $∠ B A C$ = $65^{\circ}$ and $∠ B C A$ = $75^{\circ}$ , then find $∠ R O Q$ .