Question

finding an angle measure
what is the measure of ∠a?
□°
what is the measure of ∠b?
□°
(3y + 27)°
(5y − 3)°

Explanation:

Step1: Identify parallel angle relation

In a parallelogram, opposite angles are equal, so $\angle A = \angle C$.
Set up equation: $5y - 3 = 3y + 27$

Step2: Solve for y

Subtract $3y$ from both sides: $2y - 3 = 27$
Add 3 to both sides: $2y = 30$
Divide by 2: $y = 15$

Step3: Calculate $\angle A$

Substitute $y=15$ into $\angle A$: $\angle A = 5(15) - 3 = 75 - 3 = 72$

Step4: Calculate $\angle B$

Consecutive angles in a parallelogram are supplementary: $\angle A + \angle B = 180^\circ$
Solve for $\angle B$: $\angle B = 180 - 72 = 108$

Answer:

The measure of $\angle A$ is $72^\circ$
The measure of $\angle B$ is $108^\circ$