Question

In Fig. 6.30, if AB II CD, EF I CD and
GED=126° find Z AGE, Z GEF and ZFGE.​

Answer 1

$\bold\green {✓\:verified\:answer}$

$\bold {given} \implies$

AB || CD

EF $\perp$ CD

$\angle$ GED = 126⁰

$To \: find$

$\angle$ AGE , $\angle$ GEF , $\angle$ FGE

$\boxed {solution}$

$\implies \angle$ AGE = $\angle$ GED ( Interior opposite angle )

$\therefore$ $\angle$ AGE = 126⁰

again

$\implies$ $\angle$ GEF = $\angle$ GED - $\angle$ FED

$\implies$ $\angle$ GEF = 126⁰ - 90⁰

$\therefore$ $\angle$ GEF = 36⁰

again

$\implies \angle$ FGE + $\angle$AGE = 180⁰ ( linear pair )

$\implies \angle$ FGE = 180⁰ - $\angle$ AGE

$\implies \angle$ FGE = 180⁰ - 126⁰

$\implies \angle$ FGE = 54⁰

$\huge\mathfrak\red{solved\:✓}$