Chapter 6.2, Problem 1ACYP

(a)

To determine

To find: The measure of $\angle A$ .

Answer to Problem 1ACYP

The measure of $\angle A$ is $47°$ .

Explanation of Solution

Given information: The following parallelogram is given. The angle measure of $\angle J=47°$

Calculation: Since parallelogram has opposite congruent sides. And opposite angles in a parallelogram are congruent.

Since $\angle J\cong \angle L$ , so,

  $\therefore \angle L=47°$

(b)

To determine

To find: The measure of $\angle M$ .

Answer to Problem 1ACYP

The measure of $\angle M$ is $132°$ .

Explanation of Solution

Given information: The following parallelogram is given. The measures $\angle J=47°\&\angle L=47°$ are taken from part (a).

Calculation: The sum of all the angles of a parallelogram is $360°$ .

Since $\angle J+\angle L=47+47°$ ,

  $\therefore \angle J+\angle L=96°$

  $\begin{array}{c}\therefore \angle J+\angle L+\angle M+\angle K=360°\\ \therefore \angle M+\angle K=360°-96°\\ \therefore 2\angle M=264°\left\{\because \angle M=\angle K\right\}\\ \therefore \angle M=132°\end{array}$

(c)

To determine

To find: The measure of all the angles.

Answer to Problem 1ACYP

All the angles has the same measure that is $90°$

Explanation of Solution

Given information: The measures of $\angle J$ is $90°$ .

Calculation: The sum of all the angles of a parallelogram is $360°$ . Then

  $\because \angle J=90°$

  $\therefore \angle L=90°$

Now,

  $\begin{array}{c}\therefore \angle J+\angle L+\angle M+\angle K=360°\\ \therefore \angle M+\angle K=360°-180°\\ \therefore 2\angle M=180°\left\{\because \angle M=\angle K\right\}\\ \therefore \angle M=90°\end{array}$

Therefore, all the angles has the same measure that is $90°$ .