Chapter 9.2, Problem 49SPR

To determine

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

Answer to Problem 49SPR

The value of $\angle JKL$ is $\angle JKL=80°$ .

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 $▱JKLM$ .

  $\begin{array}{c}\angle KJM=\angle KLM\mathrm{...}(1)\\ \angle JML=\angle JKL\mathrm{...}(2)\end{array}$

And,

  $\begin{array}{l}\angle KLM=\angle KLJ+\angle JLM\\ \angle KLM=70°+30°\\ \angle KLM=100°\end{array}$

Using equation (1).

  $\begin{array}{c}\angle KJM=\angle KLM\\ =100°\end{array}$

In a parallelogram, sum of all the interior angle is $360°$ .

  $\begin{array}{c}\angle KJM+\angle JKL+\angle KLM+\angle JML=360°\\ 100°+\angle JKL+100°+\angle JML=360°\\ \angle JKL+\angle JML=360°-200°\\ \angle JKL+\angle JML=160°\end{array}$

Using equation (1).

  $\angle JML=\angle JKL$

Using above equation.

  $\begin{array}{c}\angle JML+\angle JKL=160°\\ \angle JKL+\angle JKL=160°\\ 2\angle JKL=160°\\ \angle JKL=80°\end{array}$

Therefore, the value of $\angle JKL$ is $\angle JKL=80°$ .