Question

what is the measure of angle a?
a 10°
b 15°
c 90°
d 105°

Explanation:

Step1: Use the property of parallel lines

Since \( AB\parallel CD \), then \(\angle B + \angle C+\angle A= 180^{\circ}\) (the sum of interior angles on the same - side of a transversal for parallel lines). Given \(\angle B = 90^{\circ}\) and \(\angle C = 75^{\circ}\).

Step2: Calculate \(\angle A\)

Substitute the values of \(\angle B\) and \(\angle C\) into the formula \(\angle A=180^{\circ}-\angle B - \angle C\). So \(\angle A=180^{\circ}-90^{\circ}-75^{\circ}=15^{\circ}\)

Answer:

B. \(15^{\circ}\)