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3 years ago

GE bisects DGF , m_ CGD= 2x - 2, m2 EGF= 37, m CGF = 7x + 2 mZCGD = mZCGF =

Mathematics

1 answer:

stira [4]3 years ago

4 0

Answer:

m<CGD = 26°

m<CGF = 100°

Step-by-step 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°

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