Question

A rectangular sheet of paper is folded at the corner like the image. Find the value of x. What’s the answer and how do you solve?

Answer 1

X = 66°

The area folded over is a right triangle, and its void is a right triangle as well.  We have one angle marked 33° and a right angle in the bottom left.  This leaves us 180-(33+90) = 180-123 = 57°.

The folded over triangle has the same angle measurements.

We have two angles to the left of x, which form a straight angle with x.  Straight angles have a sum of 180°.  The angles that form the straight angle with x both have a measure of 57°.  This gives us:

180-(57+57) = 180-114 = 66°