Question

15 problem 15
in parallelogram hijk, the measure of angle h is 45°.

a. find the measure of angle j.
type your answer in the box.

explain how you know.

b. find the measure of angle k.
type your answer in the box.

explain how you know.

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary (sum to \(180^{\circ}\)). Angle \(H\) and angle \(J\) are adjacent.
So, \(\angle H+\angle J = 180^{\circ}\)
Given \(\angle H = 45^{\circ}\), then \(45^{\circ}+\angle J=180^{\circ}\)
\(\angle J=180^{\circ}- 45^{\circ}=135^{\circ}\)

Step2: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal. Angle \(H\) and angle \(K\) are opposite.
So, \(\angle H=\angle K\)
Since \(\angle H = 45^{\circ}\), then \(\angle K = 45^{\circ}\)

Answer:

a. \(135^{\circ}\)
b. \(45^{\circ}\)