Question

In the accompanying diagram of parallelogram ABCD, LaTeX: m\angle A=2x-10 m ∠ A = 2 x − 10 and LaTeX: m\angle B=5x+15 m ∠ B = 5 x + 15 . Find x.

Answer 1

x=?
In a parallelogram the consecutive angles must be complementary, that means they must add 180°.
In the parallelogram ABCD then angles A and B are consecutive, then:
m <A + m <B = 180°
Replacing the given angles:
(2x-10)+(5x+15)=180
2x-10+5x+15=180
Adding similar terms:
7x+5=180
Solving for x. Subtracting 5 both sides of the equation:
7x+5-5=180-5
7x=175
Dividing both sides of the equation by 7:
7x/7=175/7
x=25

Answer: x=25