Answer:
x = 28
m∠A = 76°
m∠B = 104°
Explanation:
Given the figure we can see that the two angles which measure
2x + 20 and 4x - 8 are adjacent linear angles and therefore they are supplementary angles which further means they add up to 180°
So
2x + 20 + 4x - 8 = 180
2x + 4x + 20 - 8 = 180\
6x + 12 = 180
6x = 180 - 12
6x = 168
x = 168/6
x = 28
We also have the property that angles that are vertically opposite each other at the vertex of the intersection of two lines are equal
So the angle represented by 2x + 20 = 2(28) + 20 = 56 + 20 = 76°
∠A is a vertically opposite angle to this angle and therefore the magnitude of ∠A denoted by m∠A = 76°
The angle represented by 4x - 8 = 4(28) - 8 = 112 - 8 = 104°
Since ∠B is a vertically opposite angle to this angle we have
m∠B = 104°