Using the vertical angles theorem, the value of x is calculated as: x = 7.
How to Apply the Vertical Angles Theorem?
Two angles that are vertically opposite to each other, are called vertical angles pair. The measures of the angles of a vertical angles pairs are congruent or equal to each other, based on the vertical angles theorem.
Angle A and angle B are vertical angles pairs. We are given that:
Measure of angle A = (6x − 3)°
Measure of angle B = (9x − 24)°.
Thus, the measure of angle A and the measure of angle B are congruent to each other, based on the vertical angles theorem. Therefore:
Measure of angle A = Measure of angle B
Plug in the values
6x - 3 = 9x - 24
6x - 9x = 3 - 24
-3x = -21
Divide both sides by -3
-3x/-3 = -21/-3
x = 7
Thus, based on the vertical angles theorem, the value of x is calculated as: x = 7.
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