Chapter 12, Problem 13CT

To determine

To find: The unknown angle

Answer to Problem 13CT

The unknown angle of the polygon is ${73}^{\circ }$

Explanation of Solution

Given information:

  

Calculation: From the given figure , we find the exterior angle.

We find the exterior angle of the polygon by a formula .

Formula: the sum of the exterior angle of any polygon is always ${360}^{\circ }$ .

Thus, ${\text{r}}^{\circ }+{60}^{\circ }+{68}^{\circ }+{71}^{\circ }+{88}^{\circ }={360}^{\circ }$

  $\Rightarrow {\text{ r}}^{\circ }+{287}^{\circ }={360}^{\circ }$

  $\begin{array}{l}\Rightarrow {\text{ r}}^{\circ }{\text{ = ( 360}}^{\circ }-{287}^{\circ })\\ \Rightarrow {\text{ r}}^{\circ }{\text{ = 73}}^{\circ }\end{array}$

Hence, the unknown angle of the polygon is ${73}^{\circ }$