Chapter 9.2, Problem 47SPR

To determine

To find: The value of $\angle MJK$ .

Answer to Problem 47SPR

The value of $\angle MJK$ is $\angle MJK=100°$ .

Explanation of Solution

Given information:

The given figure is shown in figure (1).

  

Figure (1)

Calculation:

In a parallelogram opposite sides are always parallel to each other.

In $▱JKLM$ , $JK$ is parallel to $ML$ and $JM$ to $LK$ .

Consider parallel lines $JK$ and $ML$ , and transverse $JL$ . Here because alternatively opposite angles are equal.

  $\begin{array}{l}\angle KJL=\angle MLJ\\ \angle KJL=30°\end{array}$

Consider parallel lines $JM$ and $KL$ , and transverse $JL$ . Here because alternatively opposite angles are equal.

  $\begin{array}{l}\angle MJL=\angle JLK\\ \angle MJL=70°\end{array}$

And,

  $\begin{array}{l}\angle MJK=\angle MJL+\angle KJL\\ \angle MJK=70°+30°\\ \angle MJK=100°\end{array}$

Therefore, the value of $\angle MJK$ is $\angle MJK=100°$ .