The value of x, based on the vertical angles theorem, is: x = 8.
How to Apply the Vertical Angles Theorem?
In the image given below, it shows that angle A and angle B are vertical angle pairs. According to the vertical angles theorem, the measures of angles that are vertical angles pairs are congruent. By being congruent, it means the measure of one angle is equal to the measure of the other.
Given the following:
m∠A = (5x − 4)° and m∠B = (8x − 28)°.
Therefore, we can state that:
Measure of angle A = measure of angle B [with reference to the vertical angles theorem]
Substitute each of the expression for angle measures to create an equation:
(5x − 4)° = (8x − 28)°
Open the bracket and solve for the value of x
5x - 4 = 8x - 28
5x - 8x = 4 - 28
-3x = -24
Divide both sides by -3
-3x/-3 = -24/-3
x = 8
Therefore, the value of x, based on the vertical angles theorem, is: x = 8.
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