Chapter SH, Problem 11.2MPS

To determine

Measures of angles.

Answer to Problem 11.2MPS

  $\angle Q=92°$ and $\angle L=92°$

Explanation of Solution

Given information:

  $\angle P=32°,\angle K=56°$

Calculation:

For identifying the other angles,

It is given that $△PQR$ and $△MLK$ are congruent.

So,

In triangle $△PQR$ and $△MLK$ ,

  $\begin{array}{l}\angle P=\angle M\\ \angle R=\angle K\end{array}$

Since $\angle P=32°,\angle K=56°$ is given and both triangles are given.

In triangle $△PQR$ ,

  $\begin{array}{l}\angle P=32°\\ \angle R=56°\\ \angle P+\angle Q+\angle R=180°\\ 32+\angle Q+56=180\\ \angle Q=92°\end{array}$

In triangle $△MLK$ ,

  $\begin{array}{l}\angle K=56°\\ \angle M=32°\\ \angle M+\angle L+\angle K=180°\\ 32+\angle L+56=180\\ \angle L=92°\end{array}$