Question

1. a parking space is in the shape of a parallelogram. the figure below is a model of the parking space. the measure of angle b is 75°. what are the measures of the other 3 angles? angle a = 105°, angle c = 105°, angle d = 75° angle a = 105°, angle c = 75°, angle d = 105° angle a = 75°, angle c = 75°, angle d = 75° angle a = 75°, angle c = 105°, angle d = 105°

Explanation:

Step1: Recall parallelogram angle - properties

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

Step2: Find angle A (adjacent to angle B)

Since angle A and angle B are adjacent, and the sum of adjacent angles in a parallelogram is 180°. Let the measure of angle A be \(x\). Then \(x + 75^{\circ}=180^{\circ}\), so \(x=180^{\circ}- 75^{\circ}=105^{\circ}\).

Step3: Find angle C (opposite to angle A)

Since opposite angles in a parallelogram are equal, angle C = angle A. So angle C = 105°.

Step4: Find angle D (opposite to angle B)

Since opposite angles in a parallelogram are equal, angle D = angle B. So angle D = 75°.

Answer:

Angle A = 105°, Angle C = 105°, Angle D = 75°