Question

in figure if AB||CD, EF is perpendicular to CD, angle FED = 90°, angle GED = 160 ° then find angle AGE, angle GEF and angle FGE​

Answer 1

$\huge\mathfrak\red{꧁Answer꧂}$

$\huge\bold{Given:}$

AB||CD , EF is perpendicular to CD, ∠FED = 90° and ∠GED = 160°

$\huge\bold{To Find:}$

∠AGE , ∠GEF , ∠FGE

$\huge\mathfrak\purple{︎︎︎Solution︎︎︎}$

Now :

AB||CD and GE is the transversal

Hence ;

∠AGE = ∠GED { Alt angle }

so ∠AGE = 160°

Now :

Since AB is the line

So;

∠AGE + ∠FGE = 180° { linear piar }

126° + ∠FGE = 180°

∠FGE = 180° - 160°

∠ FGE = 20°

Now :

Exterior angle property

So ;

∠GEF = ∠GED - ∠FED

∠GEF = 160° - 90°

∠GEF = 70°

So the value of the angles are....

∠AGE = 160°

∠ FGE = 20°

∠GEF = 70°

( refer the attachment for daigram )

Answer 2

꧁Answer꧂

Given:

AB||CD , EF is perpendicular to CD, ∠FED = 90° and ∠GED = 160°

ToFind:

∠AGE , ∠GEF , ∠FGE

Solution︎︎︎

Now :

AB||CD and GE is the transversal

Hence ;

∠AGE = ∠GED { Alt angle }

so ∠AGE = 160°

Now :

Since AB is the line

So;

∠AGE + ∠FGE = 180° { linear piar }

126° + ∠FGE = 180°

∠FGE = 180° - 160°

∠ FGE = 20°

Now :

Exterior angle property

So ;

∠GEF = ∠GED - ∠FED

∠GEF = 160° - 90°

∠GEF = 70°

So the value of the angles are....

∠AGE = 160°

∠ FGE = 20°

∠GEF = 70°

( refer the attachment for daigram )