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Given any quadrilateral, if you were to draw a line from one of its vertex to another non-adjacent vertex, this line or diagonal, will separate the quadrilateral into two triangles. The diagonal. Here the diagonal separates the quadrilateral into two triangles. The sum of the measures of the angles of a triangle is 180 degrees. Because all quadrilaterals are made up of two triangles, the sum of the measures of the angles in the quadrilateral will be 360 degrees. 100o 75o xo 130o Given the measures of the angles of the quadrilateral above, what is the measure of the angle x? Remember that the sum of the measures of the angles of the quadrilateral will add up to 360 degrees because the quadrilateral is made up of two triangles. The measure of the angles must add up to 360 degrees. Simplify and solve for x. The unknown angle must be equal to 55 degrees. If a diagonal separates the quadrilateral into two identical triangles, then the quadrilateral can be classified as a parallelogram, which means that both pairs of opposite sides are parallel and congruent.