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.

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) (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

-------------------------------------------------------

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
RELATED QUESTIONS
I need help with this question The measure of angle r is 12 degrees more than three... (answered by Seutip)

In triangle RST, an exterior angle meaure at T has a measure of 75. If measure of angle... (answered by vleith)

In quadrilateral PQRS, the measure of angle P exceeds the measure of angle Q by 10... (answered by cleomenius)

In trapezium PQRS, PQ is parallel to RS. If Angle P=120 degrees, find the measure of... (answered by rothauserc)

An exterior angle measure of a regular polygon is given. Find the number of its sides and (answered by MathLover1)

In triangle ABC, the measure of angle B is 35 degrees more than three times the measure... (answered by rfer)

(Please help?) In triangle ABC, the measure of angle B is 8 degrees more than three... (answered by ewatrrr)

An angles measure 86 degrees more than the measure of a supplementary angle. What is the... (answered by addingup)

The measure of angle A is 30 degrees less than twice the measure of angle B . Find the... (answered by Theo)