Chapter 1.2, Problem 26E

To determine

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

Answer to Problem 26E

Value of variable is $a^{\circ }={60}^{\circ }$

Measure of the polygon is ${360}^{\circ }$

Explanation of Solution

Given: Polygon is

  

Calculation:

Given the polygon as follows:

  

Since the polygon is quadrilateral, thus sum of measure of angle is equal to ${360}^{\circ }$

Thus, equation is given as

  $a^{\circ }+2a^{\circ }+a^{\circ }+2a^{\circ }={360}^{\circ }$

On solving the equation:

  $\begin{array}{l}6a^{\circ }={360}^{\circ }\\ a^{\circ }=\frac{{360}^{\circ }}{6}\\ a^{\circ }={60}^{\circ }\end{array}$

Substitute $a^{\circ }={60}^{\circ }$ in the left side of equation $a^{\circ }+2a^{\circ }+a^{\circ }+2a^{\circ }={360}^{\circ }$ to find the measure of polygon

  $\begin{array}{l}\Rightarrow {60}^{\circ }+2\left({60}^{\circ }\right)+{60}^{\circ }+2\left({60}^{\circ }\right)\\ \Rightarrow {60}^{\circ }+{120}^{\circ }+{60}^{\circ }+{120}^{\circ }\\ \Rightarrow {360}^{\circ }\end{array}$

Conclusion:

Hence, Value of variable is $a^{\circ }={60}^{\circ }$

Measure of the polygon is ${360}^{\circ }$