Find the missing side to the triangle in the attached image.

x = 2√2

Pythagorean Theorem states that in a right triangle, a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.  Thus, 4 + 4 = x^2.  Thus, x = the square root of 8, or 2√2

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true