Question

finding an angle measure
what is the measure of ∠a?
what is the measure of ∠b?

Explanation:

Step1: Use the property of parallelogram (adjacent angles are supplementary)

In a parallelogram, \( \angle A+\angle C = 180^{\circ}\). Given \( \angle A=(5y - 3)^{\circ}\) and \( \angle C=(3y + 27)^{\circ}\), we have the equation \( (5y-3)+(3y + 27)=180\).
Simplify the left - hand side: \( 5y-3+3y + 27=8y + 24\). So, \( 8y+24 = 180\).
Subtract 24 from both sides: \( 8y=180 - 24=156\).
Divide both sides by 8: \( y=\frac{156}{8}=19.5\).

Step2: Calculate \( \angle A\)

Substitute \( y = 19.5\) into \( \angle A=(5y - 3)^{\circ}\).
\( \angle A=5\times19.5-3=97.5 - 3=94.5^{\circ}\).

Step3: Calculate \( \angle B\)

Since \( \angle A+\angle B = 180^{\circ}\) (adjacent angles of a parallelogram are supplementary).
\( \angle B=180-\angle A\). Substitute \( \angle A = 94.5^{\circ}\), then \( \angle B=180 - 94.5=85.5^{\circ}\).

Answer:

The measure of \( \angle A\) is \( 94.5^{\circ}\) and the measure of \( \angle B\) is \( 85.5^{\circ}\).