Question

finding an angle measure
what is the measure of \\( \angle a \\)?
\\( \square ^ { \circ } \\)
what is the measure of \\( \angle b \\)?
\\( \square ^ { \circ } \\)

Explanation:

Step1: Use the property of consecutive angles in a parallelogram

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

Step2: Solve the equation for \(y\)

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

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

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

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

Since \(\angle A\) and \(\angle B\) are consecutive angles in a parallelogram (supplementary), \(\angle B=180 - 94.5 = 85.5\).

Answer:

\(\angle A = 94.5^{\circ}\)
\(\angle B = 85.5^{\circ}\)