Question

In the figure shown below AB || CD. If BAF
= 128°, AFC = 144° then find the measure of DCE

Answer 1

Answer:

DCE = 92°

Step-by-step explanation:

we have ,

AB | | CD

Draw a parallel line FG from point F

Therefore, AB | | FG | | CD

So,

AB | | FG and AF is transversal,

Angle A + Angle F = 180°

128° + Angle F = 180°

Angle F = 180°-128°

Angle F = 52°

Now, AFC = 144°

AFG = 52°

AFC = AFG + CFG

144° = 52° + CFG

144°- 52° = CFG

92° = CFG

So,

FG | | CD and FE is transversal,

CFG = 92°

Therefore, DCE = CFG = 92° ( Corresponding angles )

Answer 2

answer

draw a line G to H from angle F

angle BAF + angle AFH (co-interior angle)

angle AFH =180 - 128

angle AFH =52

so, angle AFE = angle AFH + angle CFH

144 = 52 + angle CFH

angle CFH = 144 -52

angle CFH = 92

therefore, angle ECD = angle CFH (corresponding angle)

angle ECD = 92