Chapter 12, Problem 10CUR

To determine

To find:The numerical measure of $\angle K$ .

Answer to Problem 10CUR

The measure of $m\angle K$ is $129°$ .

Explanation of Solution

Given information:

It is given that in $▱JKLM$ , $m\angle J=\frac{3}{2}x$ , and $m\angle L=x+17$ .

Calculation:

In parallelogram, consecutive angles are supplementary

Calculate the $m\angle k$ usingconsecutive angles properties:

  $\begin{array}{c}m\angle J+m\angle K=180°\\ \frac{3x}{2}+m\angle K=180°\\ m\angle K=180°-\frac{3x}{2}\end{array}$

Calculate the $m\angle k$ usingconsecutive angles properties:

  $\begin{array}{c}m\angle K+m\angle L=180°\\ m\angle K=180°-m\angle L\\ =180°-\left(x-17\right)\\ =163°-x\end{array}$

Calculate the value of $x$ by equate the above two equation:

  $\begin{array}{c}m\angle K=m\angle K\\ 180°-\frac{3x}{2}=163°-x\\ x=34°\end{array}$

Substitute the values in the above equation to calculate the measure of $m\angle K$ .

  $\begin{array}{c}m\angle K=163-x\\ =163°-34°\\ =129°\end{array}$

Therefore, thenumerical measure of $m\angle K$ is $129°$ .