SOLUTION: In ABCD, ∠B= (2x+y)°, ∠D= (x+2y-5)°. If ∠A= 100°, what values of x and y will make ABCD a parallelogram?

Algebra ->  Parallelograms -> SOLUTION: In ABCD, ∠B= (2x+y)°, ∠D= (x+2y-5)°. If ∠A= 100°, what values of x and y will make ABCD a parallelogram?       Log On


   

Question 1164926: In ABCD, ∠B= (2x+y)°, ∠D= (x+2y-5)°. If ∠A= 100°, what values of x and y will make ABCD a parallelogram?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
In a parallelogram, the opposite angles are equal. If angle A = 100, then angle C = 100
The other two angles must sum to 360 - 100 - 100 = 160.
Thus each angle is 80:
x + 2y - 5 = 80
2x + y = 80 -> y = 80 - 2x
x + 2(80 - 2x) - 5 = 80
3x = 75 -> x = 25
Thus y = 80 - 50 = 30
x = 25, y = 30