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cricket20 [7]
3 years ago
10

In parallelogram RSWY, find m

Mathematics
1 answer:
LuckyWell [14K]3 years ago
8 0

Answer:

Part A) m\angle R=110^o

Part B) m\angle S=70^o

Step-by-step explanation:

we know that

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

step 1

Find the value of x

we know that

m\angle R=m\angle W ----> by definition of parallelogram (opposite angles are congruent)

substitute the given values

(5x-90)^o=(2x+30)^o

solve for x

5x-2x=30+90\\3x=120\\x=40^o

step 2

Find the measure of angle R

m\angle R=(5x-90)^o

substitute the value of x

m\angle R=(5(40)-90)=110^o

step 3

Find the measure of angle S

we know that

m\angle R+m\angle S=180^o ---> by definition of parallelogram (consecutive angles are supplementary)

we have

m\angle R=110^o

substitute

110^o+m\angle S=180^o

m\angle S=180^o-110^o

m\angle S=70^o

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