To solve this, we need to know what vertical angles and what supplementary angles are. Vertical angles are each of the pairs of opposite angles made by two intersecting lines. And, by the Vertical Angles Theorem, we know that they have the same measure. Now onto supplementary angles. Supplementary angles are angles that add up to 180 degrees.
Let's say that one of the vertical angles is equal to x. That means that the other one is also equal to x, and their sum is 2x. Since we are trying to find out a situation where vertical angles are supplementary, or equal to 180 degrees, that means that 2x is equal to 180 degrees. This is satisfied <em>only </em>when x = 90 degrees, meaning that vertical angles are supplementary when they are right angles.
It is given that the triangle is isosceles right triangle . And in an isosceles right triangle the legs are equal . Let each leg be of x units. Now we use pythagorean identity, which is
