Question

In the given figure, O is the center of the circle and AC the diameter. The line FEG is tangent to the circle at point E. If ∠GEC = 52°, find the value of ∠e + ∠c.

(a) 154° 

(b) 156° 

(c) 166° 

(d) 180°

Answer 1

Answer : (c) 166º 

∠OAE = ∠GEC = 52° (Angles in alternate segments are equal)

∠AEC = 90° (Angle in a semi circle)

∴  In ∆ ACE, e = ∠ACE = 180° – (90° + 52°) = 38° 

ACDE is a cyclic quadrilateral

⇒ c = ∠EDC = 180° – ∠CAE 

= 180° – 52° = 128° (opp. ∠s of a cyclic quad. are supp.) 

∴  c + e = 128° + 38° = 166°.