Question

Find the value of xin the figure. Then find the unknown angle measures.

Short answer

The value of $x$ is $6°$.

Step-by-step solution

Step 1. Given Information.

The figure is given below.

Step 2. Calculation.

Since, a right angle is an angle which is equal to $90°$. Therefore,

$8x{}^{\circ }+42{}^{\circ }=90°$ …… (1)

Find x using equation (1).

$\begin{array}{c}8x°+42°=90°\\ 8x°=90°-42°\\ 8x°=48°\\ x=\frac{48°}{8°}\end{array}$

This implies that,

$x=6°$

Thus, the value of x is $6°$.

Step 3. Conclusion.

The measures of unknown angles are $48{}^{\circ }\text{and}42°$.