If m∠FAB = 48° and m∠ECB = 18°, what is m∠ABC?

C. 66°

Step-by-step explanation:

Given:

m∠FAB = 48°,

m∠ECB = 18°,

Required:

m∠ABC

SOLUTION:

∠CHB ≅ ∠FAB (alternate interior angles theorem)

m∠CHB = ∠FAB

m∠CHB = 48° (substitution)

m∠CHB + m∠ECB + m∠CBH = 180° (sum of angles in a ∆)

48° + 18° + m∠CBH = 180° (substitution)

66° + m∠CBH = 180°

Subtract 66° from each side

m∠CBH = 180° - 66°

m∠CBH = 114°

Thus,

m∠CBH + m∠ABC = 180° (Linear pair)

114° + m∠ABC = 180° (substitution)

Subtract 114° from both sides

m∠ABC = 180° - 114°

m∠ABC = 66°

oof

step-by-step explanation: