Question

The measure of angle CFD is The measure of angle CDF is The measure of angle AFB is The measure of angle BFD is The measure of angle ABC is

Answer 1

∠CDF = 23° , ∠CFD = 115° , ∠AFB = 115° , ∠BFD = 65° , ∠ABC = 42°

Explanation:

m∠CDF = 180 - m∠CDE

m∠CDF = 180 - 157

m∠CDF = 23°

m∠CFD = 180 - ( m∠DCF + m∠CDF )

m∠CFD = 180 - ( 42 + 23 )

m∠CFD = 115°

m∠AFB = m∠CFD (Vertically opposite angles)

m∠AFB = 115°

m∠BFD = 180 - m∠CFD

m∠BFD = 180 - 115

m∠BFD = 65°

∠ABC

Solution 1:

m∠ABC = m∠DCF (Alternate angles)

m∠ABC = 42°

Solution 2:

In ΔAFB

m∠FAB = m∠CDF (Alternate angles)

m∠FAB = 23°

m∠ABC = 180 - ( m∠AFB + m∠FAB )

m∠ABC = 180 - ( 115 + 23 )

m∠ABC = 42°