Question

In fig., if AB।। CD, EF is perpendicular to CD and/_GED=126*, find /_AGE, /_GEF and/_FGE.​

Answer 1

Answer :-

Given :-

AB | | CD

EF is perpendicular to CD

∠GED = 126°

Required to find :-

• ∠AGE

• ∠GEF

• ∠FGE

Solution :-

Given that :-

AB | | CD

EF is perpendicular to CD

∠GED = 126°

Consider,

AB | | CD

GE is the transversal

So,

∠GED = ∠AGE ( Alternate interior angles )

Hence

∠AGE = 126°

Similarly,

∠GEF + ∠FED = ∠GED

So,

∠GEF = ∠GED - ∠FED

∠GEF = 120° - ∠FED

Since EF is perpendicular to CD

∠FED = 90°

Hence,

∠GEF = 120° - 90°

∠GEF = 30°

Now consider ∆ GEF

In ∆ GEF

∠FGE+ ∠GEF + ∠GFE = 180°

∠FGE + 30° + ∠GFE = 180°

Since, EF is perpendicular to CD

∠GFE = 90°

So,

∠FGE + 30° + 90° = 180°

∠FGE + 120° = 180°

∠FGE = 180° - 120°

∠FGE = 60°

Therefore,

• ∠AGE = 126°

• ∠GEF = 30°

• ∠FGE = 60°

Answer 2

✰✰ ANSWER ✰✰

➮Given : -

• AB // CD
• EF Perpendicular to CD
• $\implies\tt{\angle{GED}=126\degree}$

➮To find : -

• $\implies\tt{\angle{AGE}=?}$
• $\implies\tt{\angle{GEF}=?}$
• $\implies\tt{\angle{EGF}=?}$

➥Now ,

$\implies\tt{\angle{AGE}=\angle{GED}(Alternale\:Angles)}$

$\implies\tt{\angle{AGE}=126\degree}$

$\implies\tt{\angle{GED}=\angle{GEF}+\angle{FED}}$

$\implies\tt{126\degree=\angle{GEF}+90\degree}$

$\implies\tt{126\degree-90\degree=\angle{GEF}}$

$\implies\tt{\angle{GEF}=36\degree}$

➥Also ,

$\implies\tt{\angle{AGE}+\angle{EGF}=180\degree(Linear\:Pair)}$

$\implies\tt{126\degree+\angle{EGF}=180\degree}$

$\implies\tt{\angle{EGF}=180\degree-126\degree}$

$\implies\tt{\angle{EGF}=54\degree}$

➥So ,

$\implies\tt{\angle{AGE}=126\degree}$

$\implies\tt{\angle{GEF}=36\degree}$

$\implies\tt{\angle{EGF}=54\degree}$