Question

Find the value of x.

Short answer

The value of x is$\mathbf{76}°$.

Step-by-step solution

Step 1. Given Information.

The figure is shown below.

Step 2. Formula used.

The angle sum properties of quadrilateral is as follows:

$\angle A+\angle B+\angle D+\angle C=360°$

Step 3. Calculation.

According to angle sum properties of quadrilateral,

$\angle A+\angle B+\angle D+\angle C=360°$

Substituting the value of angles,

localid="1652665524771" $\begin{array}{c}(2x-17)°+90°+x°+59°=360°\\ 3x+90°+42°=360°\\ 3x+132°=360°\\ 3x=228\end{array}$

On further simplification,

localid="1652665537585" $\begin{array}{c}x=\left(\frac{228}{3}\right)°\\ =76°\end{array}$

Angles are;

localid="1652665555922" $\begin{array}{c}\angle C=x°\\ =76°\end{array}$

And,

localid="1652665571638" $\begin{array}{c}\angle A=\left(2x-17\right)°\\ =2\times 76°-17°\\ =152°-17°\\ =135°\end{array}$

Step 3. Conclusion.

The value of x is$76°$.