Chapter 7.6, Problem 37SPR

To determine

Find the value of the given measurement using kite diagram.

Answer to Problem 37SPR

The value of the given measurement is $m\angle K={117}^{°}$ .

Explanation of Solution

Given:

The given measurement is $m\angle K$ and the given diagram is

  

Calculation:

In a kite,one pair of opposite angles are congruent.

  $\angle j\cancel{\cong }\angle L$ (given)

So, $\angle M\cong \angle K$

In a quadrilateral, the sum of all angles $={360}^{°}$

Let $m\angle M=m\angle K=x$

Now,

  $\begin{array}{l}m\angle J+m\angle L+m\angle M+m\angle K={360}^{°}\\ \Rightarrow {59}^{°}+{67}^{°}+x+x={360}^{°}\\ \Rightarrow {126}^{°}+2x={360}^{°}\\ \Rightarrow {126}^{°}+2x-{126}^{°}={360}^{°}-{126}^{°}\\ \Rightarrow 2x={234}^{°}\\ \Rightarrow \frac{2}{2}x=\frac{{234}^{°}}{2}\\ \Rightarrow x={117}^{°}\end{array}$

Hence the value of the given measurement is $m\angle K={117}^{°}$ .