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In given fig. if AB || CD, EF CD and GED = 126^o, find AGE,

Question

In given fig. if $A B ∣∣ C D, EF ⊥ C D$ and $∠ GE D = 12 6^{o}$ , find $∠ A GE, ∠ GEF$ and $∠ FGE$ .

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Levi Discussed

In given fig. if

A B ∣∣ C D, EF ⊥ C D

and

∠ GE D = 12 6^{o}

, find

∠ A GE, ∠ GEF

and

∠ FGE

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Text solutionVerified

Given,

A B ∥ C D

EF ⊥ C D

∠ GE D = 12 6^{\circ}

According to the question,

∠ FE D = 9 0^{\circ}

(EF ⊥ C D)

Now,

∠ A GE = ∠ GE D

(Since,

A B ∥ C D

and

GE

is transversal. Alternate interior angles.)

∴ ∠ A GE = 12 6^{\circ}

Also,

∠ GEF = ∠ GE D - ∠ FE D

\Rightarrow ∠ GEF = 12 6^{\circ} - 9 0^{\circ}

\Rightarrow ∠ GEF = 3 6^{\circ}

Now,

∠ FGE + ∠ A GE = 18 0^{\circ}

(Linear pair)

\Rightarrow ∠ FGE = 18 0^{\circ} - 12 6^{\circ}

\Rightarrow ∠ FGE = 5 4^{\circ}

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Question Text	In given fig. if $A B ∣∣ C D, EF ⊥ C D$ and $∠ GE D = 12 6^{o}$ , find $∠ A GE, ∠ GEF$ and $∠ FGE$ .
Answer Type	Text solution:1
Upvotes	150