Question

a parallelogram has one angle that measures 105.3°. what are the measures of the other three angles in the parallelogram? °, °, and °

Explanation:

Step1: Recall parallelogram angle - properties

In a parallelogram, opposite angles are equal and adjacent angles are supplementary (sum to 180°).

Step2: Find an adjacent angle

Let the given angle $\theta = 105.3^{\circ}$. An adjacent angle $\alpha$ satisfies $\theta+\alpha = 180^{\circ}$. So, $\alpha=180 - 105.3=74.7^{\circ}$.

Step3: Determine the other angles

The angle opposite the given 105.3° angle has the same measure, 105.3°. The angle opposite the 74.7° angle also has a measure of 74.7°.

Answer:

74.7, 105.3, 74.7