The value of x is 184.
What is the value of x?
Given Information
The measure of angle 2 = 92°
The measure of angle 4 = (x/2)°
From the figure, it can be seen that angle 2 and 4 make vertically opposite angles.
Vertically Opposite Angles
The pair of angles that are formed by two intersecting lines and are opposite to each other are defined as vertically opposite angles. The values of vertically opposite angles are always equal.
Here, in this case, ∠1 and ∠3 make a pair of vertically opposite angles. ∠2 and ∠4 form another pair of vertically opposite angles. Hence,
∠4 = ∠2
(x/2) = 92
x = 92 × 2
x = 184
Thus, the value of x is 184.
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