The expression m∠ FCE tells us to find the measure of the angle between two rays, CF and CE. We have marked this angle in the figure below.
From the figure we can deduce that A, C and D lie on the same line, so ∠ ACD is a straight angle. Thus, m∠ ACD= 180. Let's also observe that
angles ∠ ACF and ∠ DCE are congruent.
m∠ FCA = m∠ DCE
The sum of m∠ FCA, m∠ FCE and m∠ DCE is equal to m∠ ACD. We will also include our observation about congruence to simplify the expression.
m∠ FCA+ m∠ FCE+ m∠ DCE= m∠ ACD
⇕
m∠ FCA + m∠ FCE + m∠ FCA = m∠ ACD
We know that m∠ ACD = 180. From the exercise we also know that m∠ FCA = 50.
Let's substitute these facts into our equation and solve for m∠ FCE.
