Question

find m∠tuv if m∠tuv = x + 135, m∠tuf = 60°, and m∠fuv = 2x + 75.

Explanation:

Step1: Use angle addition postulate

From the diagram, we know that \( m\angle TUV = m\angle TUF + m\angle FUV \). Substituting the given expressions, we get:
\( x + 135 = 60 + (2x + 75) \)

Step2: Simplify the equation

Simplify the right - hand side: \( 60+2x + 75=2x + 135 \)
So the equation becomes \( x + 135=2x + 135 \)

Step3: Solve for x

Subtract \( x \) from both sides: \( 135=x + 135 \)
Then subtract 135 from both sides: \( x = 0 \)

Step4: Find \( m\angle TUV \)

Substitute \( x = 0 \) into \( m\angle TUV=x + 135 \)
\( m\angle TUV=0 + 135=135^{\circ} \)

Answer:

\( 135^{\circ} \)