In parallelogram RSWY, find m

Question

asked Jul 15, 2021 40.1k views

1 Answer

Bill K · Answer 1 · 2021-07-20T02:57:45+0000

Answer:

Part A)
$m\angle R=110^o$

Part B)
$m\angle S=70^o$

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

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

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

$m\angle S=70^o$