Chapter 12.2, Problem 5C

To determine

To calculate: The measurement of the angles:

  $m\angle 1$ , $m\angle 2$ , $m\angle 3$ , $m\angle 4$ , $m\angle 5$ , $m\angle 6$ and $m\angle 7$ .

Answer to Problem 5C

The measurement of the angles are,

  $m\angle 1={58}^{\circ }$ , $m\angle 2={122}^{\circ }$ , $m\angle 3={58}^{\circ }$ , $m\angle 4={58}^{\circ }$ , $m\angle 5={122}^{\circ }$ , $m\angle 6={122}^{\circ }$ and $m\angle 7={58}^{\circ }$

Explanation of Solution

Given information:

  

The measurement of one angle in the diagram is ${122}^{\circ }$ .

Concept used:

  $\angle 1+\angle 2={180}^{\circ }$ (Straight angle) ,

  $\angle 1=\angle 3$ (vertically opposite angle),

  $\angle 4=\angle 7$ (vertically opposite angle),

  $\angle 5=\angle 6$ (vertically opposite angles) ,

  $\angle 1=\angle 4$ (Corresponding angles) and $\angle 2=\angle 6$ (Corresponding angles).

Calculation:

  $\begin{array}{l}{122}^{\circ }+m\angle 1={180}^{\circ }\\ \Rightarrow m\angle 1={180}^{\circ }-{122}^{\circ }\\ \Rightarrow m\angle 1={58}^{\circ }\end{array}$

So, $m\angle 2={122}^{\circ }$

  $m\angle 3={58}^{\circ }$ ,

  $m\angle 4={58}^{\circ }$ ,

  $m\angle 5={122}^{\circ }$ ,

  $m\angle 6={122}^{\circ }$ ,

  $m\angle 7={58}^{\circ }$

The measurement of the angles are,

  $m\angle 1={58}^{\circ }$ , $m\angle 2={122}^{\circ }$ , $m\angle 3={58}^{\circ }$ , $m\angle 4={58}^{\circ }$ , $m\angle 5={122}^{\circ }$ , $m\angle 6={122}^{\circ }$ and $m\angle 7={58}^{\circ }$