Question

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 = 75°, angle d = 105° angle a = 75°, angle c = 75°, angle d = 75° angle a = 105°, angle c = 105°, angle d = 75°

Explanation:

Step1: Properties of parallelogram

In a parallelogram, opposite angles are equal. So, if \(\angle B = 75^{\circ}\), then \(\angle D=\angle B = 75^{\circ}\) (opposite angles).

Step2: Adjacent angles in parallelogram

Adjacent angles in a parallelogram are supplementary (\(\angle A+\angle B = 180^{\circ}\)). Given \(\angle B = 75^{\circ}\), then \(\angle A=180^{\circ}-\angle B\).

$$ \angle A=180 - 75=105^{\circ} $$

Since \(\angle A\) and \(\angle C\) are opposite angles in the parallelogram, \(\angle C=\angle A = 105^{\circ}\)

Answer:

Angle \(A = 105^{\circ}\), Angle \(C = 105^{\circ}\), Angle \(D = 75^{\circ}\) (the third option)