Question

what is the measure of ∠a? what is the measure of ∠b? (3y + 27)° (5y - 3)°

Explanation:

Step1: Use property of parallelogram

In a parallelogram, adjacent - angles are supplementary, so $\angle A+\angle B = 180^{\circ}$. Also, $\angle A=(5y - 3)^{\circ}$ and $\angle B=(3y + 27)^{\circ}$. Then, $(5y - 3)+(3y + 27)=180$.

Step2: Simplify the equation

Combine like - terms: $5y+3y-3 + 27=180$, which gives $8y+24 = 180$.

Step3: Solve for y

Subtract 24 from both sides: $8y=180 - 24=156$. Then, divide both sides by 8: $y=\frac{156}{8}=19.5$.

Step4: Find the measure of $\angle A$

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

Step5: Find the measure of $\angle B$

Substitute $y = 19.5$ into the expression for $\angle B$: $\angle B=(3\times19.5 + 27)^{\circ}=(58.5+27)^{\circ}=85.5^{\circ}$.

Answer:

The measure of $\angle A$ is $94.5^{\circ}$.
The measure of $\angle B$ is $85.5^{\circ}$.