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) degree
s and angle A is (5 y minus 3) degrees. What is the measure of ∠A? ° What is the measure of ∠B? °
1 answer:
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

solve for y



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°
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