Option 3:
m∠ABC = 66°
Solution:
Given [tex]\overline {F A D} \| \overline {E H C}[/tex] and ABH is a transversal line.
m∠FAB = 48° and m∠ECB = 18°
m∠ECB = m∠HCB = 18°
Property of parallel lines:
If two parallel lines cut by a transversal, then the alternate interior angles are equal.
m∠FAB = m∠BHC
48° = m∠BHC
m∠BHC = 48°
Exterior angle of a triangle theorem:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
m∠ABC = m∠BHC + m∠HCB
m∠ABC = 48° + 18°
m∠ABC = 66°
Option 3 is the correct answer.
