Question

the given figure, if AB || CD, and ∠HEB = 60°, ∠BEG = 40°, ∠GFD = 30°.Find ∠EGF, ∠AEF and ∠EFC.​

Answer 1

As per the diagram, lines CD∣∣EF and CE is transveral.

We know that sum of interior angles is equal to 180o

∠ECD+∠CEF=180°

∠ECD+130°=180°

∠ECD=180−130°

∠ECD=50°

As per the diagram, lines AB∣∣CD and CA is transveral.

We know that alternate angles are equal.

∠BAC=∠ACD 

∠BAC=∠ACE+∠ECD

70°=∠ACE+50°

20°=∠ACE

∴∠ACE=20°