The value of x is 16.
We are given that:
Angle 1 measures 78 degrees: ∠1 = 78°
Angle 3 measures (5x-2) degrees: ∠3 = (5x-2)°
Since vertical angles are congruent, we know that angle 1 and angle 3 are equal in measure. Therefore:
Angle 1 = Angle 3
78 degrees = 5x - 2 degrees
To solve for x, we need to isolate it.
1. Add 2 degrees to both sides:
78 degrees + 2 degrees = 5x - 2 degrees + 2 degrees
80 degrees = 5x
2. Divide both sides by 5:
80 degrees / 5 = 5x / 5
16 = x
Therefore, the value of x is 16.
Complete question:
If the measure of angle 1 is 78 degrees and the measure of angle 3 is (5x-2)degrees, what is the value of x ?