Question

If AB || CD, EF ⊥ CD and ∠GED = 135° as per the figure given below.

Find the value of ∠AGE?​

Answer 1

Answer:

Given,

AB∥CD, EF⊥CD, ∠GED=126

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According to the question,

∠FED=90

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(EF⊥CD)

Now,

∠AGE=∠GED (Since, AB∥CD and GE is transversal. Alternate interior angles.)

∴∠AGE=126

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Also,

∠GEF=∠GED−∠FED

⇒∠GEF=126

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−90

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⇒∠GEF=36

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Now,

∠FGE+∠AGE=180

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(Linear pair)

⇒∠FGE=180

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−126

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⇒∠FGE=54

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