Question

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

Answer 1

Answer:

m∠ CGD = 22°

Step-by-step 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

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

$angle(EGF)=40$