Question : In a $\triangle$PQR, the side QR is extended to S. If $\angle$QPR = 72° and $\angle$PRS=110°, then the value of $\angle$PQR is:
Option 1: 38°
Option 2: 32°
Option 3: 25°
Option 4: 29°
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Correct Answer: 38°
Solution :
Given: $\angle$QPR = 72° and $\angle$PRS = 110°
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
So, $\angle PQR + \angle QPR =\angle PRS$
⇒ $\angle PQR + 72° = 110°$
⇒ $\angle PQR = 110° - 72° = 38°$
Hence, the answer is 38°.
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