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

Question

Quadrilateral ABCD ~ quadrilateral HJKL.

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

Answer 1

Since figure ABCD is a quadrilateral:

m∠A + m∠B + m∠C + m∠D = 360°

We are given that:

∠B ≅ ∠J, so m∠B = m∠J

∠C ≅ ∠K, so m∠C = m∠K

So we can replace B with J and C with K:

m∠A + m∠B + m∠C + m∠D = 360°

m∠A + m∠J + m∠K + m∠D = 360°

x + x+50 + 2x-55 + x+45 = 360

Solve for x.