Question

What is m CGD = 4x + 2, m DGE = 3x - 5, m EGF = 2x + 10

Answer 1

m∠ CGD = 22°

Explanation:

In the figure attached, m∠CGD = 4x + 2, m∠DGE = 3x - 5 and ,m∠ EGF = 2x + 10

Now it is given in figure, m∠DGE ≅ m∠EGF

Now we equate the values of angles

3x - 5 = 2x + 10

3x - 2x = 10 - 5

x = 5

∠CGD = 4x + 2

for x = 15

∠CGD = 4×15 + 2

= 60 + 2

= 62°

Therefore, m∠CGD = 62° is the answer.

Answer 2

Calculation of x:

we can see that

angle(DGE)=angle(EGF)

we are given

angle(DGE)=3x-5

angle(EGF)=2x+10

now, we can set them equal

`3x-5=2x+10`

now, we can solve for x

`3x-5+5=2x+10+5`

`3x=2x+15`

subtract both sides 2x

`3x-2x=2x+15-2x`

`x=15`

now, we can find angles

Calculation of angle(CGD):

`angle(CGD)=4x+2`

we can plug x=15

`angle(CGD)=4*15+2`

`angle(CGD)=62`

Calculation of angle(DGE):

`angle(DGE)=3x-5`

we can plug x=15

`angle(DGE)=3*15-5`

`angle(DGE)=40`

Calculation of angle(EGF):

`angle(EGF)=2x+10`

we can plug x=15

`angle(EGF)=2*15+10`

`angle(EGF)=40`