Question

Find the measure of angle x in the figure below: A:35 B:48 C:69 D:78

Answer 1

The best way to solve for x is to first solve for y and then subtract values. The top of "line" of the 3 angles togethers add up to 180 degrees. So from this, you can deduct this equation into $52+59+y=180$. To solve for y, subtract $52$ and $59$ from the left hand side and rights hand side of the equation. now you know the value is $y=180-52-59=69$. So the value of y is 69 degrees. 
Now you know two angles of a triangle and the sum of the angles in a triangle is 180 degrees. So the equation is $x+69+63=180$. To solve for x, subtract $69+63$ from both sides. $x=180-69-63=48$. So you know that $x=48$ degrees.