Chapter 5.6, Problem 10PSA

To determine

To calculate:Themeasure of each angle in parallelogram OJKM.

Answer to Problem 10PSA

The measure of each angleis ${145}^{\circ }$ .

Explanation of Solution

Given information:

In a parallelogram OJKM,

Angle $y=3x+40$

Calculation:

  

In parallelogram OJKM,

Angles x and y are supplementary to each other. There sum is 180 degrees.

The measure of x angle:

  $\begin{array}{l}x+y={180}^{\circ }\\ y=3x+{40}^{\circ }\\ x+3x+{40}^{\circ }={180}^{\circ }\\ 4x={180}^{\circ }-{40}^{\circ }\\ 4x={140}^{\circ }\\ x=\frac{{140}^{\circ }}{4}={35}^{\circ }\end{array}$

The measure of yangle:

  $\begin{array}{l}y=3x+{40}^{\circ }\\ y=\left(3\times {35}^{\circ }\right)+{40}^{\circ }\\ y=\left({105}^{\circ }\right)+{40}^{\circ }\\ y={145}^{\circ }\end{array}$