Answer:
∠CDF = 23° , ∠CFD = 115° , ∠AFB = 115° , ∠BFD = 65° , ∠ABC = 42°
Step-by-step 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°
