Question

21. In figure, If AB II CD, EF is perpendicular to CD, ∠FED = 90⁰

∠GED = 116⁰, then find ∠AGE, ∠ GEF and∠ FGE .​

Answer 1

∠AGE = 116°

∠ GEF = 26°

∠ FGE = 64°

Explanation:

Given:

• AB║CD
• EF║CD
• ∠FED = 90°
• ∠GED = 116°

As

• AB║CD

Then

∠GED = ∠AGE (Alternate Interior angles)

∠FGE = ∠GEC (Alternate Interior angles)

Therefore,

∠AGE = ∠GED = 116° each

Now,

∠GED + ∠GEC = 180°  [Linear pair]

⇒ 116 + ∠GEC = 180°

⇒ ∠GEC = 180° - 116°

⇒ ∠GEC = 64°

So,

∠GEC = ∠FGE =  64°

----

Also,

∠GEF + ∠GEC = 90°   [As EF ⊥ CD]

⇒ ∠GEF + 64 = 90

⇒ ∠GEF = 90 - 64

⇒ ∠GEF = 26°

Answer 2

Answer:

∠AGE = 116°

∠ GEF = 26°

∠ FGE = 64°

Explanation:

Given:

AB║CD

EF║CD

∠FED = 90°

∠GED = 116°

As

AB║CD

Then

∠GED = ∠AGE (Alternate Interior angles)

∠FGE = ∠GEC (Alternate Interior angles)

Therefore,

∠AGE = ∠GED = 116° each

Now,

∠GED + ∠GEC = 180°  [Linear pair]

⇒ 116 + ∠GEC = 180°

⇒ ∠GEC = 180° - 116°

⇒ ∠GEC = 64°

So,

∠GEC = ∠FGE =  64°

----

Also,

∠GEF + ∠GEC = 90°   [As EF ⊥ CD]

⇒ ∠GEF + 64 = 90

⇒ ∠GEF = 90 - 64

⇒ ∠GEF = 26°