$∠ A$ and $∠ B$ are vertically opposite angles, and $∠ A = 5 x$ and $∠ B = 90 ° + 2 x$ . Find the value of $x$ .

30°

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60°

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90°

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120°

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Solution

The correct option is A 30°
Given: $∠ A$ and $∠ B$ are vertically opposite angles.
$∠ A = 5 x$
$∠ B = 90 ° + 2 x$
We know that when two lines intersect each other, the vertically opposite angles thus formed are equal.
$\Rightarrow ∠ A = ∠ B$
$\Rightarrow 5 x = 90 ° + 2 x$
$\Rightarrow 3 x = 90 °$
$\Rightarrow x = 30 °$

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