If m∠A = x°, m∠ J = (x + 50)°, m∠D = (x + 45)°, and m∠K = (2x − 55)°, find x°.

Question

If m∠A = x°, m∠ J = (x + 50)°, m∠D = (x + 45)°, and m∠K = (2x − 55)°, find x°.

Quadrilateral ABCD ~ quadrilateral HJKL.

Answer 1

Since they are similar, m<B = m<J = x + 50 and m<C = m<K = 2x - 55 We are already given the measure of angle A and D. The sum of the angles of any quadrilateral is 360 degrees, so sum those measures and solve for x.