$in the given figure, A B | | C D a n d E F is a transversal, cutting them at G and H respectively. if ∠ E G B = 35^{\circ} a n d Q P ⊥ E F, find the measure of ∠ P Q H .$

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Solution

ANSWER:In the given figure, AB || CD and EF is a transversal.
∴ $∠ P H Q = ∠ E G B$
(Pair of alternate exterior angles)
⇒ $∠ P H Q = 35^{\circ}$
In $△ P H Q$
$∠ P H Q + ∠ Q P H + ∠ P Q H = 180^{\circ}$
(Angle sum property)
⇒ $35 ° + 90 ° + x = 180^{\circ}$
⇒ $125 ° + x = 180^{\circ}$
⇒ $x = 180 ° - 125 ° = 55^{\circ}$
Thus, the measure of $∠ P Q H i s 55^{\circ}$

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in the given figure,AB||CD and EFis a transversal, cutting them at G and H respectively. if ∠EGB=35∘and QP⊥EF,find the measure of ∠PQH.

ANSWER:In the given figure, AB || CD and EF is a transversal. ∴ ∠PHQ=∠EGB (Pair of alternate exterior angles) ⇒ ∠PHQ=35∘ In △PHQ ∠PHQ+∠QPH+∠PQH=180∘ (Angle sum property) ⇒ 35°+90°+x=180∘ ⇒ 125°+x=180∘ ⇒ x=180°−125°=55∘ Thus, the measure of ∠PQHis55∘

$in the given figure, A B | | C D a n d E F is a transversal, cutting them at G and H respectively. if ∠ E G B = 35^{\circ} a n d Q P ⊥ E F, find the measure of ∠ P Q H .$