Find:m∠FCE in degrees

Question

Consider the following figure.

.

Given:AB ∥ DC, m∠A = m∠B = 54°,

CE ∥ DA, and CF bisects ∠DCB

Find:m∠FCE in degrees

Answer 1

Because m<A = m<B, ABCD is an isosceles trapezoid.

The lower and upper base angles of an isosceles trapezoid are supplementary, so m<DCB = 180 - 54 = 126.

Since CF bisects <DCB, m<FCE = half m<DCB = 63.