Question

in the diagram below, $fd \parallel ec$. if $m\angle fab = 48^\circ$ and $m\angle ecb = 18^\circ$, what is $m\angle abc$?
a. $18^\circ$
b. $48^\circ$
c. $66^\circ$
d. $114^\circ$

Explanation:

Step1: Draw auxiliary line through B

Draw line $BG \parallel FD$ (so $BG \parallel EC$ since $FD \parallel EC$)

Step2: Find $\angle ABG$

By alternate interior angles, $\angle ABG = \angle FAB = 48^\circ$

Step3: Find $\angle CBG$

By alternate interior angles, $\angle CBG = \angle ECB = 18^\circ$

Step4: Sum angles for $\angle ABC$

$\angle ABC = \angle ABG + \angle CBG$
$\angle ABC = 48^\circ + 18^\circ = 66^\circ$

Answer:

C. $66^\circ$