Question

in parallelogram hijk, the measure of angle h is 45°.a. find the measure of angle j.type the answer in the box below.angle j has a measure of 45.explain how you know.type your response in the space below.all angles are the sameb. find the measure of angle k.type the answer in the box below.angle k has a measure of.explain how you know.type your response in the space below.

Explanation:

Step1: Properties of parallelogram

In a parallelogram, consecutive angles are supplementary (sum to \(180^{\circ}\)) and opposite angles are equal.

Step2: Find measure of angle \(J\)

Since \(HIJK\) is a parallelogram, \(\angle H\) and \(\angle J\) are consecutive angles. So \(\angle H+\angle J = 180^{\circ}\). Given \(\angle H = 45^{\circ}\), then \(\angle J=180^{\circ}-\angle H\).

$$ \angle J = 180^{\circ}- 45^{\circ}=135^{\circ} $$

Step3: Find measure of angle \(K\)

In a parallelogram, \(\angle H\) and \(\angle K\) are opposite angles. Opposite angles of a parallelogram are equal. So \(\angle K=\angle H\)

$$ \angle K = 45^{\circ} $$

Answer:

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