Chapter 5.1, Problem 28WE

To determine

To Find: the measure of $\angle 2$ in a parallelogram DECK shown in figure such that $m\angle 1=42,m\angle 2=x^2\text{ and }m\angle CED=13x$ .

Answer to Problem 28WE

  $49$ or $\text{ 36}$

Explanation of Solution

Given

  $m\angle 1=42,m\angle 2=x^2\text{ and }m\angle CED=13x$ .

and figure is.

  

Calculation:

Since, opposite angles in a parallelogram are congruent.

  $\begin{array}{l}\angle K=\angle E\\ \angle 1+\angle 2=\angle CED\\ 42+x^2=13x\\ x^2-13x+42=0\\ x^2-7x-6x+42=0\\ \left(x-7\right)\left(x-6\right)=0\\ x=6\text{or}7\end{array}$

Now, $m\angle 2$ .

  $\begin{array}{l}m\angle 2=x^2\\ m\angle 2=7^2=49\text{and}m\angle 2=6^2=36\\ m\angle 2=49\text{or 36}\end{array}$

Therefore, the answer is $49\text{and 36}$