By applying the vertical angles theorem, the value of x in the diagram is determined as: x = 7.
What is the Vertical Angles Theorem?
The vertical angles theorem states that, if two angles (e.g. angles A and B in the image given), are vertically opposite each other, they are vertical angles and their angle measure would be the same or congruent to each other.
This implies that the measures of angles A and B in the image given are equal to each other (congruent angles). We are given that:
m∠A = (6x − 3)°
m∠B = (9x − 24)°
Make both angles equal to each other in other according to the vertical angles theorem:
m∠A = m∠B
Substitute
6x - 3 = 9x - 24
Solve for x
6x - 9x = 3 - 24
-3x = -21
-3x/-3 = -21/-3
x = 7
Thus, based on the vertical angles theorem, the value of x in the diagram is: 7.
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