Answer:
m<CGD = 26°
m<CGF = 100°
Explanation:
m<CGD = 2x - 2
m<EGF = 37
m<CGF = 7x + 2
Since GE bisects <DGF, m<DGF = 2*m<EGF.
m<DGF = 2*37 = 74°
m<CGD + m<DGF = m<CGF (angle addition postulate)
(2x - 2) + (74) = (7x + 2)
Find the value of x using the equation above.
2x - 2 + 74 = 7x + 2
Collect like terms
2x + 72 = 7x + 2
-2 + 72 = 7x - 2x
70 = 5x
70/5 = 5x/5
14 = x
x = 14
m<CGD = 2x - 2
Plug in the value of x
m<CGD = 2(14) - 2 = 28 - 2
m<CGD = 26°
m<CGF = 7x + 2
m<CGF = 7(14) + 2 = 98 + 2
m<CGF = 100°