Question

find m∠yxz

Explanation:

Step1: Use the property of parallel lines and transversal

Since \( UV\parallel WY \) and \( TZ \) is a transversal, \( \angle VSY=\angle YXZ \) (corresponding angles). Also, \( \angle VSY = 7x + 8 \) and \( \angle YXZ=4x + 30.8 \). So, \( 7x+8=4x + 30.8 \).

Step2: Solve the equation for \( x \)

Subtract \( 4x \) from both sides: \( 7x-4x+8=4x-4x + 30.8 \), which gives \( 3x+8=30.8 \).
Subtract \( 8 \) from both sides: \( 3x+8 - 8=30.8 - 8 \), so \( 3x=22.8 \).
Divide both sides by \( 3 \): \( x=\frac{22.8}{3}=7.6 \).

Step3: Find \( m\angle YXZ \)

Substitute \( x = 7.6 \) into \( 4x+30.8 \).
\( 4\times7.6+30.8=30.4+30.8=61.2 \).

Answer:

\( 61.2^{\circ} \)