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
[tex]3x-5=2x+10[/tex]
now, we can solve for x
[tex]3x-5+5=2x+10+5[/tex]
[tex]3x=2x+15[/tex]
subtract both sides 2x
[tex]3x-2x=2x+15-2x[/tex]
[tex]x=15[/tex]
now, we can find angles
Calculation of angle(CGD):
[tex]angle(CGD)=4x+2[/tex]
we can plug x=15
[tex]angle(CGD)=4*15+2[/tex]
[tex]angle(CGD)=62[/tex]
Calculation of angle(DGE):
[tex]angle(DGE)=3x-5[/tex]
we can plug x=15
[tex]angle(DGE)=3*15-5[/tex]
[tex]angle(DGE)=40[/tex]
Calculation of angle(EGF):
[tex]angle(EGF)=2x+10[/tex]
we can plug x=15
[tex]angle(EGF)=2*15+10[/tex]
[tex]angle(EGF)=40[/tex]
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.
