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

Answer:

Part a) m∠A=72°

Part b) m∠B=108°

Step-by-step 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°