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In the following image, find x in degrees.

Guest Dec 1, 2019

hectictar · Answer 1 · 2019-12-02T12:21:16

Because they form a straight line,

m∠GFC + m∠GFB = 180°

m∠GFC = 180° – m∠GFB

m∠GFC = 180° – 140°

m∠GFC = 40°

Because the sum of interior angles in △CGF is 180°,

m∠GFC + m∠GCF + m∠CGF = 180°

40° + 59° + 3y° = 180°

3y° = 81°

y = 27

Because the sum of interior angles in △CGE is 180°,

m∠GEC + m∠GCE + m∠CGE = 180°

x° + 59° + 2y° = 180°

x° + 59° + 2(27)° = 180°

x° + 59° + 54° = 180°

x° = 180° – 59° – 54°

x° = 67°