Chapter 12.2, Problem 19E

To determine

To calculate: the angles: $m\angle 1$ , $m\angle 2$ and $m\angle 3$ .

Answer to Problem 19E

The measurement of the angles are, $m\angle 1={90}^{\circ }$ , $m\angle 2={115}^{\circ }$ , $m\angle 3={65}^{\circ }$ .

Explanation of Solution

Given information : Two angles of the given diagram are ${115}^{\circ }$ and ${90}^{\circ }$ .

Concept used: $m\angle 3+{115}^{\circ }={180}^{\circ }$ (Sum of linear pair angles are ${180}^{\circ }$ ) , ${90}^{\circ }+m\angle 1={180}^{\circ }$ (Sum of consecutive interior angles are ${180}^{\circ }$ ), $m\angle 2+m\angle 3={180}^{\circ }$ (Sum of consecutive interior angles are ${180}^{\circ }$ ).

Calculation :

  $\begin{array}{l}m\angle 3+{115}^{\circ }={180}^{\circ }\\ \Rightarrow m\angle 3={180}^{\circ }-{115}^{\circ }\\ \Rightarrow m\angle 3={65}^{\circ }\end{array}$

  $\begin{array}{l}{90}^{\circ }+m\angle 1={180}^{\circ }\\ \Rightarrow m\angle 1={180}^{\circ }-{90}^{\circ }\\ \Rightarrow m\angle 1={90}^{\circ }\end{array}$

  $\begin{array}{l}m\angle 2+m\angle 3={180}^{\circ }\\ \Rightarrow m\angle 2={180}^{\circ }-m\angle 3\\ \Rightarrow m\angle 2={180}^{\circ }-{65}^{\circ }\\ \Rightarrow m\angle 2={115}^{\circ }\end{array}$

Hence, the measurement of $m\angle 1={90}^{\circ }$ , $m\angle 2={115}^{\circ }$ , $m\angle 3={65}^{\circ }$ .