Question

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

Answer 1

Answer:
x = 55

Explanation:
In a parallelogram, the sum of each two consecutive angles is 180°.

In the given parallelogram ABCD, we can note that angles A and B are consecutive angles. This means that their summation is 180°

Therefore:
∠A + ∠B = 180
2x + 15 + x = 180
3x + 15 = 180
3x = 180 - 15
3x = 165
x = 165 / 3
x = 55

Now we can check:
angle A = 2(55) + 15 = 125°
angle B = 55°
angle A + angle B = 125 + 55 = 180°

Hope this helps :)