Chapter 1.6, Problem 6PSA

To determine

To Prove: $\angle 1\cong \angle 2$

Explanation of Solution

Given:

  

  $\begin{array}{l}\angle 1\text{ is obtuse}\\ \angle 2\text{ is acute}\end{array}$

Concept Used:

Sum of linear pairs of angles is $180°$

Proof:

Here, we have

  $\begin{array}{l}\angle 1\text{ is obtuse}\\ \Rightarrow 90<1<180\\ \angle 2\text{ is acute}\\ \Rightarrow 0<2<90\\ \Rightarrow 90°<\angle 1+\angle 2<270°\end{array}$

But,

  $\begin{array}{l}\angle 1+\angle 2=180°\\ \Rightarrow \angle 1\cong \angle 2\end{array}$