If m∠B = 30°, m∠C = x°, and m∠AFB = (4x)°, find x°.

Question

△ABF ~ △CBD with obtuse angles at vertices D and F as indicated.

If m∠B = 30°, m∠C = x°, and m∠AFB = (4x)°, find x°.

Answer 1

If the two triangles are similar, then their corresponding internal angles have equal measure. Since angle B is common to both triangles, we have m∠C = m∠A. For triangle ABC:

m∠A + m∠B + m∠AFB = 180°

Since m∠C = m∠A:

m∠C + m∠B + m∠AFB = 180°

x + 30 + 4x = 180

Solve for x.