Question

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

Explanation:

Step1: Identify the property of the quadrilateral

The figure appears to be a parallelogram (indicated by the parallel - side markings). In a parallelogram, adjacent angles are supplementary, i.e., $\angle A+\angle B = 180^{\circ}$, and $\angle A=\angle C$, $\angle B=\angle D$. So, $(5y - 3)+(3y + 27)=180$.

Step2: Solve the equation for $y$

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

Step3: Find the measure of $\angle A$

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

Step4: Find the measure of $\angle B$

Since $\angle A+\angle B = 180^{\circ}$ in a parallelogram, $\angle B=180-\angle A$. So, $\angle B=180 - 94.5 = 85.5^{\circ}$.

Answer:

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