Question

1. find m∠muv if m∠tum = x + 121, m∠muv = x + 32, and m∠tuv = 141°.

Explanation:

Step1: Use angle - addition postulate

Since $\angle TUV=\angle TUM+\angle MUV$, we have the equation $(x + 121)+(x + 32)=141$.

Step2: Combine like - terms

$x+x+121 + 32=141$, which simplifies to $2x+153 = 141$.

Step3: Solve for $x$

Subtract 153 from both sides: $2x=141 - 153=-12$. Then divide both sides by 2, so $x=-6$.

Step4: Find $m\angle MUV$

Substitute $x = - 6$ into the expression for $m\angle MUV$. Since $m\angle MUV=x + 32$, then $m\angle MUV=-6+32 = 26^{\circ}$.

Answer:

$26^{\circ}$