Mathematics Question on Lines Parallel to the Same Line

Question

In Figure, if AB $||$ CD, EF $⊥$ CD and $∠$ GED=126°, find $∠$ AGE, $∠$ GEF and $∠$ FGE.
AB||CD,EF⊥CD

Accepted Answer

It is given that, AB $||$ CD.
EF $⊥$ CD
$∠$ GED = 126º
$⇒$ ∠GEF + $∠$ FED = 126º
$⇒$ $∠$ GEF + 90º = 126º
$⇒$ $∠$ GEF = 36º
$∠$ AGE and $∠$ GED are alternate interior angles.
$⇒$ $∠$ AGE = $∠$ GED = 126º

However, $∠$ AGE + $∠$ FGE = 180º (Linear pair)
$⇒$ 126º + $∠$ FGE = 180º
$\Rightarrow$$∠$ FGE = 180º − 126º = 54º
∴ $∠$ AGE = 126º, $∠$ GEF = 36º, $∠$ FGE = 54º