If the value of - AOE -35- then find the value of - BOC-A- 35-B- 45-C- 55-D- 65-

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Vertically Opposite Angles

If the value ...

Question

If the value of $∠ A O E = 35 °$ , then find the value of $∠ B O C .$

35°

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45°

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55°

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65°

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Solution

The correct option is C 55°

Given $∠ A O B = 90 °, ∠ A O E = 35 °$ .

$∠ A O E = ∠ D O C = 35 °$ (Vertically opposite angles)

From the figure, we know that,
$∠ A O B + ∠ B O D = 180 °$ ( Linear pair)
$\Rightarrow 90 ° + ∠ B O D = 180 °$
$\Rightarrow ∠ B O D = 180 ° - 90 ° = 90 °$

But,
$∠ B O D = ∠ B O C + ∠ O C D$
$\Rightarrow 90 ° = ∠ B O C + 35 °$
$\Rightarrow ∠ B O C = 90 ° - 35 ° = 55 °$

Hence the value of $∠ B O C = 55 °$

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If the value of ∠AOE=35°, then find the value of ∠BOC.

If the value of $∠ A O E = 35 °$ , then find the value of $∠ B O C .$