Answer:
x = 52 degrees
Step-by-step explanation:
Let's first focus on the angle x + 72. Immediately adjacent to x + 72 is angle RQS. These two angles are "straight" in that they lie immediately adjacent to one another and add up to 180 degrees. Then angle RQS can be expressed as
180 degrees - (x + 72 degrees), or 108 - x degrees.
The three interior angles of the triangle must add up to 180 degrees. Hence
108 - x degrees + 34 degrees + 90 degrees = 180 degrees, and so:
108 - x + 34 = 90
This yields x = 52 degrees.
