Answer
x = 50 degrees.
Explanation
To solve this, we need to first explain vertically opposite angles.
Vertically opposite angles are angles that are directly opposite each other at the point where two lines cross each other. And vertically opposite angles are equal to each other if the two line crossing each other are straight lines.
From the image attached, we can see that
(3y - 50) and (2y + 10) are vertically opposite angles. So,
3y - 50 = 2y + 10
3y - 2y = 10 + 50
y = 60 degrees
Also noting that the sum of angles at a point is 360 degrees.
The unlabelled fourth space is a vertically opposite angle with x. So, we can write that
x + x + 3y - 50 + 2y + 10 = 360
2x + 5y - 40 = 360
Recall that y = 60 degrees
2x + 5y - 40 = 360
2x + 5 (60) - 40 = 360
2x + 300 - 40 = 360
2x + 260 = 360
2x = 360 - 260
2x = 100
Divide both sides by 2
(2x/2) = (100/2)
x = 50 degrees.
Hope this Helps!!!
