Question

Please help me. It’s geometry

Answer 1

Option 3:

m∠ABC = 66°

Solution:

Given $\overline {F A D} \| \overline {E H C}$ 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.