Question

1. find x if m∠tum = x + 80, m∠muv = x + 67, and m∠tuv = 143°.

Explanation:

Step1: Use angle - addition postulate

Since $\angle TUV=\angle TUM+\angle MUV$, we can write the equation $(x + 80)+(x + 67)=143$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side: $2x+147 = 143$.

Step3: Isolate the variable term

Subtract 147 from both sides of the equation: $2x=143 - 147$, so $2x=-4$.

Step4: Solve for $x$

Divide both sides by 2: $x=\frac{-4}{2}=-2$.

Answer:

$x=-2$