Question

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

Short answer

The value of $x$ is $15°$.

Step-by-step solution

Step 1. Given Information.

The figure is given below.

Step 2. Calculation.

Since, sum of the angles forming a linear pair is $180°$. Therefore,

$5x{}^{\circ }+7x{}^{\circ }=180°$ …… (1)

Find x using equation (1).

$\begin{array}{c}5x°+7x°=180°\\ 12x°=180°\\ x=\frac{180°}{12°}\\ x=15°\end{array}$

Thus, the value of x is $15°$.

Step 3. Conclusion.

The measures of unknown angles are $75°$ and $105°$.