Chapter 12, Problem 12CT

To determine

To find: The measure of the $\angle {\text{q}}^{\circ }$ .

Answer to Problem 12CT

The measure of the unknown angle $\angle {\text{q}}^{\circ }$ is ${140}^{\circ }$ .

Explanation of Solution

Given information:

  

Calculation:

The given figure is a $7\text{-gon}$ which is seven sided polygon.

The sum of the interior angles of a polygon $=(\text{n}-2)\times {180}^{\circ }$

Where, for the $7\text{-gon}$

  $\text{n}=7$

The sum of the interior angles of the $7\text{-gon}$ is,

  $\begin{array}{l}=(\text{n}-2)\times {180}^{\circ }\\ =(7-2)\times {180}^{\circ }\\ ={900}^{\circ }\end{array}$

Therefore, $\text{q}+{129}^{\circ }+{120}^{\circ }+{137}^{\circ }+{143}^{\circ }+{141}^{\circ }+{90}^{\circ }={900}^{\circ }$$\mathrm{......}(1)$

Let’s find the value of the unknown angle from the equation $(1)$ ,

  $\begin{array}{c}\text{q}+{129}^{\circ }+{120}^{\circ }+{137}^{\circ }+{143}^{\circ }+{141}^{\circ }+{90}^{\circ }={900}^{\circ }\\ \text{q}+{760}^{\circ }={900}^{\circ }\\ \text{q}={900}^{\circ }-{760}^{\circ }\\ \text{q}={140}^{\circ }\end{array}$

Hence, The measure of the unknown angle $\angle {\text{q}}^{\circ }$ is ${140}^{\circ }$ .