Question

1. abcd is a parallelogram.

find the measure of ∠c.
find the measure of ∠a.
find the measure of ∠d.

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal. So, \(\angle B=\angle D\) and \(\angle A = \angle C\). Given \(\angle B=110^{\circ}\), but we need to find \(\angle C\) first. Wait, no, actually, adjacent angles in a parallelogram are supplementary (\(\angle A+\angle B = 180^{\circ}\), \(\angle B+\angle C=180^{\circ}\), \(\angle C+\angle D = 180^{\circ}\), \(\angle D+\angle A=180^{\circ}\)) and opposite angles are equal (\(\angle A=\angle C\), \(\angle B=\angle D\))

Step2: Find \(\angle C\)

Since \(ABCD\) is a parallelogram, \(\angle A+\angle B=180^{\circ}\) and \(\angle B + \angle C=180^{\circ}\). Wait, no, opposite angles: \(\angle A=\angle C\), \(\angle B=\angle D\). Adjacent angles: \(\angle A+\angle B = 180^{\circ}\). But if we consider \(\angle B = 110^{\circ}\), and \(\angle A+\angle B=180^{\circ}\), then \(\angle A=70^{\circ}\). Since \(\angle A=\angle C\), \(\angle C = 70^{\circ}\)

Step3: Find \(\angle A\)

As \(\angle A+\angle B=180^{\circ}\) (adjacent angles of a parallelogram are supplementary), and \(\angle B = 110^{\circ}\), then \(\angle A=180^{\circ}- 110^{\circ}=70^{\circ}\)

Step4: Find \(\angle D\)

Since \(\angle B=\angle D\) (opposite angles of a parallelogram are equal), and \(\angle B = 110^{\circ}\), then \(\angle D=110^{\circ}\)

Answer:

The measure of \(\angle C\) is \(70^{\circ}\), the measure of \(\angle A\) is \(70^{\circ}\), and the measure of \(\angle D\) is \(110^{\circ}\)