angle question

[median badge]

Why are both of these angles (denoted as theta) equal?

[zenith citrus]

Move the dashed rectangle so that its upper corner is at the same position as the right vertex on the large triangle.

With the bottom drawing, you start with theta as the angle inside the triangle. Then, that's part of a right angle, so you have 90 degrees minus theta there. Then, that new angle and the rectangle's upper left angle sum to a right angle, so it's 90 degrees - (90 degrees - theta), which is theta.

[scarlet plume]

hi