Chapter 1.2, Problem 25E

To determine

To calculate: To find the value of the variable and the find the measure of the polygon

Answer to Problem 25E

Value of variable is $k^{\circ }={45}^{\circ }$

Measure of the polygon is ${180}^{\circ }$

Explanation of Solution

Given: Polygon is

  

Calculation:

Given the polygon as follows:

  

Here, sum of polygon is equal to $180$

Thus, equation is given as

  $45+2k+k=180$

On solving the equation:

  $\begin{array}{l}2k+k=180-45\\ 3k^{\circ }=135\\ k^{\circ }=\frac{135}{3}\\ k^{\circ }=45\end{array}$

Substitute $k^{\circ }={45}^{\circ }$ in the left side of equation $45+2k+k=180$ to find the measure of polygon

  $\begin{array}{l}\Rightarrow 45+2\left({45}^{\circ }\right)+{45}^{\circ }\\ \Rightarrow 45+{90}^{\circ }+{45}^{\circ }\\ \Rightarrow {180}^{\circ }\end{array}$

Conclusion:

Hence, Value of variable is $k^{\circ }={45}^{\circ }$

Measure of the polygon is ${180}^{\circ }$