Question

IF AB||CD, EF perpendicular CD and Angle GED=126°,find AGE, Angle GEF and FGE​

Answer 1

ANSWER:-

GIVEN:

ABIICD, EF perpendicular CD, Angle GED=126º

We have to find:

Angle AGE, Angle GEF, Angle FGE

Therefore,

angle AGE=angle GED (alternate interior angles)

angle AGE = 126º

angle GED = angle GEF + angle FED

126º = angle GEF + 90º

angle  GEF = 126º - 90º = 36º

angle GEF = 36º

angle AGE + angle FGE = 180º (linear pair)

126º + angle FGE = 180º

angle FGE = 180º - 126º

angle FGE = 54º

THANKS!!!

Answer 2

Step-by-step explanation:

GEF + FEG = GED

EF ? CD so that FED = 90

And given that GED = 126

GEF + 90 = 126

GEF = 126- 90

GEF = 36

AB || CD, EF ? CD so EFG = 90

Use angle sum property of triangle (sum is 180)

GEF + EFG + FGE = 180

Plug the values we get

36+ 90+ FGE = 180

FGE = 180 36- 90

FGE = 54

AB is a straight line so that use linear pair property

AGE +FGE = 180

Plug the value of FGE = 54

We get

AGE +54= 180

AGE = 180- 54

AGE = 126