Question

1. ( mangle fuv = x + 55 ), ( mangle tuf = 90^circ ), and ( mangle tuv = 2x + 145 ). find ( mangle tuv ).

Explanation:

Step1: Analyze angle addition

From the diagram, \( m\angle TUV = m\angle TUF + m\angle FUV \). Substitute the given expressions: \( 2x + 145 = 90 + (x + 55) \).

Step2: Solve for \( x \)

Simplify the right - hand side: \( 2x + 145 = x + 145 \). Subtract \( x \) from both sides: \( 2x - x+ 145=x - x + 145\), so \( x=0 \).

Step3: Find \( m\angle TUV \)

Substitute \( x = 0 \) into \( m\angle TUV=2x + 145 \): \( m\angle TUV=2(0)+145 = 145^{\circ} \).

Answer:

\( 145^{\circ} \)