Question

what is the measure of ∠a?
what is the measure of ∠b?

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, consecutive angles are supplementary. So, \((5y - 3)+(3y + 27)=180\).

Step2: Solve the equation for \(y\)

Combine like terms: \(5y+3y-3 + 27=180\), \(8y+24 = 180\).
Subtract 24 from both sides: \(8y=180 - 24\), \(8y=156\).
Divide by 8: \(y=\frac{156}{8}=19.5\).

Step3: Find the measure of \(\angle A\)

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

Step4: Find the measure of \(\angle B\)

Since \(\angle A\) and \(\angle B\) are supplementary (in a parallelogram \(AD\parallel BC\)), \(\angle B=180-\angle A\)
\(\angle B=180 - 94.5=85.5\)

Answer:

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