Question

= A C F xº E G 80° 160° D B

Answer 1

The value of angle ∠AEF or ∠x is 80°.

What are angles?

• When two straight lines or rays intersect at a common endpoint, an angle is formed.
• An angle's vertex is the common point of contact.
• The term angle is derived from the Latin word angulus, which means "corner."
• The basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation.

So,

• ∠CEB is 160° with EG being an angle bisector leaving ∠CEG = 80° and ∠BEG = 80°
• FEG is a straight line with ∠FEG being 180°.
• ∠FED + ∠DEB + ∠BEG = ∠FEG
• 80° + ∠DEB + 80° = 180°
• 160° + ∠DEB = 180°
• ∠DEB = 180° - 160°
• ∠DEB = 20°

Then,

• ∠AEC = 20° = ∠DEB (Inversely opposite angles)

Now,

• FEG is a straight line with ∠FEG being 180°.
• ∠CEG + ∠AEC + ∠AEF = ∠FEG
• 80° + 20° + ∠AEF = 180°
• 100° + x = 180°
• x = 180° - 100°
• x = 80°
• ∠AEF = 80°

Therefore, the value of angle ∠AEF or ∠x is 80°.

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