In the given figure, if $∠ D O B$ = 2x - 5° and $∠ A O C$ = 85°, then x = ___.

$85^{\circ}$

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$15^{\circ}$

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$45^{\circ}$

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$35^{\circ}$

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Solution

The correct option is C
$45^{\circ}$

Given: $∠ A O C = 85^{\circ}$
$∠ D O B = 2 x - 5^{\circ}$

Here, AB and CD intersect at O.
We know that when two lines intersect, vertically opposite angles are equal.
$\Rightarrow ∠ A O C = ∠ D O B$
$\Rightarrow 85^{\circ} = 2 x - 5^{\circ}$
$\Rightarrow 2 x = 90^{\circ}$
$\Rightarrow x = 45^{\circ}$

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