Question

Parallelogram A B C D is shown. Sides A B and D C are parallel, and sides A D and B C are parallel. Angle C is (3 y + 27) degrees and angle A is (5 y minus 3) degrees. What is the measure of ∠A? ° What is the measure of ∠B? °

Answer 1

∠A=72

∠B=108

Explanation:

Answer 2

Part a) m∠A=72°

Part b) m∠B=108°

Explanation:

we know that

In a parallelogram opposite angles are congruent and consecutive angles are supplementary

so

In this problem

m∠A=m∠C

m∠A+m∠B=180°

step 1

Find the value of y

m∠A=m∠C

substitute the given values

`(5y-3)\°=(3y+27)\°`

solve for y

`5y-3y=27+3`

`2y=30`

`y=15`

step 2

Find the measure of angle A

m∠A=(5y-3)°

substitute the value of y

m∠A=(5(15)-3)=72°

step 3

Find the measure of angle B

m∠A+m∠B=180°

we have

m∠A=72°

substitute

72°+m∠B=180°

m∠B=180°-72°

m∠B=108°