A) 100 degrees
b) 50 degrees
c) 65 degrees
d) 30 degrees

a) 100 degrees

Step-by-step explanation:

EFG + EGD + DGC = 180  since the form a straight line

EGD = 30 since it is a vertical angle to AGB = 30

DGC = 50

Substitute these values in

EFG +30 + 50 = 180

Combine like terms

EFG +80 = 180

Subtract 80 from each side

EFG +80-80 = 180-80

EFG =100

use formula for the circle a=3.14

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)