Chapter 12.3, Problem 22E

To determine

To find : the $\angle 1$ form by William street and George street and $\angle 2$ which is form by bisects William street and Olaf street.

Answer to Problem 22E

The $m\angle 1$ form by William street and George street is ${120}^{\circ }$ and $m\angle 2$ form by bisects William street and Olaf street is ${120}^{\circ }$ .

Explanation of Solution

Given : consider, the hexagonprovided in the question,

Formula used:

the measure of an interior angle of a regular n -gon is $\frac{\left(n-2\right)·{180}^{\circ }}{n}$ .

the measure of an exterior angle at vertex = ${180}^{\circ }$ -interior angle at that vertex

Calculation: to find the $m\angle 1$ formed by William street and George street, substitute the n by 6 because the given figure is hexagon.

the measure of an interior angle of a regular hexagon is $\begin{array}{l}\frac{\left(6-2\right)·{180}^{\circ }}{6}\text{ [substitute n by 6]}\\ \frac{4·{180}^{\circ }}{6}\text{ [subtract]}\\ {120}^{\circ }\text{ [multiply and divide]}\end{array}$ .

All interior angles are same so,

$m\angle 1$ = ${120}^{\circ }$

After bisects the William street and Olaf street, the interior angle will be the half of the interior angle,

So

  $\begin{array}{l}m\angle 2+{60}^{\circ }={180}^{\circ }\text{ [substitute]}\\ m\angle 2={180}^{\circ }-{60}^{\circ }\text{ [subtract]}\\ m\angle 2={120}^{\circ }\end{array}$

Hence,The $m\angle 1$ form by William street and George street is ${120}^{\circ }$ and $m\angle 2$ form by bisects William street and Olaf street is ${120}^{\circ }$ .