Question

I don’t understand how to do it ?

Answer 1

We know that Sum of Angles in a Triangle is Equal to 180°

Here EBF is a Triangle

⇒ m∠EBF + m∠BEF + m∠EFB = 180°

⇒ 60° + 40° + m∠EFB = 180°

⇒ 100° + m∠EFB = 180°

⇒ m∠EFB = 180° - 100°

⇒ m∠EFB = 80°

As Line m and Line p are Parallel Lines :

Alternate Interior Angles are Equal, here Alternate Interior Angles are m∠BEF and m∠ABE

⇒ m∠BEF = m∠ABE

⇒ m∠ABE = 40°

We know that Vertically Opposite Angles are Equal, Here m∠GFI and m∠EFB are Vertically Opposite Angles.

⇒ m∠GFI = m∠EFB

⇒ m∠GFI = 80°

We can notice that m∠DEB and m∠BEF form a Linear Pair

⇒ m∠DEB + m∠BEF = 180°

⇒ m∠DEB + 40° = 180°

⇒ m∠DEB = 180° - 40°

⇒ m∠DEB = 140°

We can notice that Sum of Angles m∠CBF and m∠EBF and m∠ABE is 180°

⇒ m∠CBF + m∠EBF + m∠ABE = 180°

⇒ m∠CBF + 60° + 40° = 180°

⇒ m∠CBF + 100° = 180°

⇒ m∠CBF = 180° - 100°

⇒ m∠CBF = 80°

We can notice that m∠BFG and m∠EFB form a Linear Pair

⇒ m∠BFG + m∠EFB = 180°

⇒ m∠BFG + 80° = 180°

⇒ m∠BFG = 180° - 80°

⇒ m∠BFG = 100°

We know that Vertically Opposite Angles are Equal, Here m∠BFG and m∠IFE are Vertically Opposite Angles.

⇒ m∠BFG = m∠IFE

⇒ m∠IFE = 100°