Question

in the figure below, $overleftrightarrow{cd}$ intersects $overleftrightarrow{ab}$ at $f$, $mangle cfb = 50^circ$, and $angle efa cong angle afd$. what is $mangle efc$? 70° 40° 50° 80°

Explanation:

Step1: Find $m\angle AFD$

Vertical angles are equal, so $m\angle AFD = m\angle CFB = 50^\circ$.

Step2: Find $m\angle EFA$

Given $\angle EFA \cong \angle AFD$, so $m\angle EFA = 50^\circ$.

Step3: Calculate $m\angle EFD$

Sum the two angles: $m\angle EFD = m\angle EFA + m\angle AFD = 50^\circ + 50^\circ = 100^\circ$.

Step4: Find $m\angle EFC$

Linear pair sums to $180^\circ$, so $m\angle EFC = 180^\circ - m\angle EFD = 180^\circ - 100^\circ = 70^\circ$.

Answer:

70°