Question

1. find m∠hiw if m∠wij = 10x, m∠hij = 145°, and m∠hiw = 2x + 13.

Explanation:

Step1: Use angle - addition postulate

Since $\angle HIJ=\angle HIW+\angle WIJ$, we can write the equation $145=(2x + 13)+10x$.

Step2: Combine like - terms

Combining the $x$ terms on the right - hand side, we get $145 = 12x+13$.

Step3: Isolate the variable term

Subtract 13 from both sides: $145−13=12x$, so $132 = 12x$.

Step4: Solve for $x$

Divide both sides by 12: $x=\frac{132}{12}=11$.

Step5: Find $m\angle HIW$

Substitute $x = 11$ into the expression for $m\angle HIW$: $m\angle HIW=2x + 13=2\times11+13$.
$m\angle HIW=22 + 13=35$.

Answer:

$35^{\circ}$