Question

one angle of a parallelogram measures 30°. what are the measures of the other three angles in the parallelogram?

Explanation:

Step1: Recall parallelogram properties

In a parallelogram, opposite - angles are equal and adjacent - angles are supplementary.

Step2: Find the opposite angle

The angle opposite to the given 30° angle is equal to it. So one of the other angles is 30°.

Step3: Find the adjacent angles

Let the adjacent angle to the 30° angle be \(x\). Since adjacent angles in a parallelogram are supplementary (\(x + 30^{\circ}=180^{\circ}\)), then \(x = 180^{\circ}-30^{\circ}=150^{\circ}\). The other adjacent angle (opposite to the first - found adjacent angle) is also 150° because opposite angles in a parallelogram are equal.

Answer:

30, 150, 150