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Lines and Angles
Question
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In figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75°, find ∠SQT.

Answer

In ∆PRT,
∠PTR + ∠PRT + ∠RPT = 180°
| ∵ The sum of all the angles of a triangle is 180°
⇒ ∠PTR + 40°+ 95° = 180°
⇒    ∠PTR + 135° = 180°
∠    ∠PTR = 45°
⇒    ∠QTS = ∠PTR = 45°
| Vertically Opposite Angles
In ∆TSQ,
∠QTS + ∠TSQ + ∠SQT = 180°
| ⇒ The sum of all the angles of a triangle is 180°
⇒ 45° + 75° + ∠SQT = 180°
⇒ 120° + ∠SQT = 180°
⇒    ∠SQT = 180° - 120° = 60°.

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