SOLUTION: So I have a parallelogram (the top is A B the bottom is D C) and angle A says (3x+10)andlge B says (8x+5) angle D says 5y. angle C says nothing. I was wondering how I am supposed t

Algebra ->  Polygons -> SOLUTION: So I have a parallelogram (the top is A B the bottom is D C) and angle A says (3x+10)andlge B says (8x+5) angle D says 5y. angle C says nothing. I was wondering how I am supposed t      Log On


   

Question 739768: So I have a parallelogram (the top is A B the bottom is D C) and angle A says (3x+10)andlge B says (8x+5) angle D says 5y. angle C says nothing. I was wondering how I am supposed to solve this when andlge D and B have diff letter names and nothing matches A. Thanks:)
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
we are given the parallelogram ABDC which means that AB is parallel to DC, furthermore opposite angles are equal which means
Angle A is equal to angle C and angle D is equal to angle B, also angles A and D add up to 180 degrees (supplementary angles) as well as angles B and C. So we have the following equations.
3x+10+5y=180
8x+5+angle C =180
but angle C = angle A so
8x+5+3x+10=180
11x+15=180
11x=165
x=15
substituting for x in equation one, we have
3*15 + 10 + 5y = 180
55 + 5y = 180
5y = 125
y = 25
so x = 15 and y = 25
that means angle A = 3 * 15 + 10 = 55, angel B = 8 * 15 + 5 = 125
angle D = 5 * 25 = 125 and angle C = angle A =55