Question

find x, then find the measurement of both angles.

Explanation:

Step1: Set angles equal (corresponding angles)

$2x + 54 = 4x - 6$

Step2: Isolate x terms

$54 + 6 = 4x - 2x$

Step3: Simplify and solve for x

$60 = 2x \implies x = \frac{60}{2} = 30$

Step4: Calculate first angle

$2(30) + 54 = 60 + 54 = 114$

Step5: Calculate second angle

$4(30) - 6 = 120 - 6 = 114$

Answer:

$x = 30$
Measure of both angles: $114^\circ$