In the figure, ΔDEG and ΔEGF are isosceles; ∠EDG = 64º. Find the following (give reasons): a) ∠DGE. b) ∠EGF. c) The value of x d) ∠HEF

A.) 64°

B) 116°

C.) 32°

Step-by-step explanation:

Given that ΔDEG and ΔEGF are isosceles ;

∠EDG = 64º

Therefore ∠EDG = ∠DGE = 64º (Base Angle of an isosceles triangle are equal)

B.) ∠EGF + ∠DGE =180° (SUM OF ∠s on a straight line)

∠EGF + 64° = 180°

∠EGF = (180 - 64) = 116°

C.) x° = ∠EDG (BASE angles of an isosceles triangle are the same)

2x° + 116° = 180° (sum of angles in a triangle)

2x = 64°

x = 32°