Chapter 1.6, Problem 5PSA

To determine

To Prove: $\angle D\cong \angle C$

Explanation of Solution

Given:

  

  $\begin{array}{l}\angle D\text{is obtuse}\text{.}\\ \angle C>90°\end{array}$

Concept Used:

Measure of obtuse angle is greater than $90°$ while less than $180°$

Proof:

Here, we have

  $\begin{array}{l}\angle D\text{is obtuse}\text{.}\\ 90°<\angle D<180°\\ \because \angle C>90°,\text{but }\angle C<180°\\ \Rightarrow 90°<\angle C<180°\\ \Rightarrow \angle D\cong \angle C\end{array}$