SOLUTION: In Parallelogram PQRS, measure of angle R is 24 degrees more than measure of angle S. Find the measure of each interior angle. HELP.

Algebra ->  Parallelograms -> SOLUTION: In Parallelogram PQRS, measure of angle R is 24 degrees more than measure of angle S. Find the measure of each interior angle. HELP.       Log On


   

Question 707251: In Parallelogram PQRS, measure of angle R is 24 degrees more than measure of angle S. Find the measure of each interior angle. HELP.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Angle S = x degrees

Angle R = x+24 degrees

Angles R and S are adjacent angles since they are next to each other

Adjacent angles in any parallelogram are supplementary, so...

m < R + m < S = 180

(x+24) + (x) = 180

x+24 + x = 180

2x + 24 = 180

2x = 180-24

2x = 156

x = 156/2

x = 78

x+24 = 78 + 24 = 102

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Answer:

Angle S = 78 degrees

Angle R = 102 degrees

Angle P is opposite angle R, so Angle P = 102 degrees

This is because opposite angles of any parallelogram are congruent.

Angle Q is opposite angle S, so Angle Q = 78 degrees