In figure, if PQ ⊥ PS, PQ || SR,
∠SQR = 28° and ∠QRT = 65°, then find the values of x and y.
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- ∠SQR = 28°
- ∠QRT = 65°
- Value of x and y
∠SQR +∠QRT = 180° [ Linear Pair ]
➨∠SQR + 65° = 180°
➨∠SQR = 180° - 65°
➨∠SQR = 115°
∠SQR + ∠SRQ + ∠QSR = 180° [Angle Sum Property of triangle ]
➨ 28° + 115° + ∠QSR = 180°
➨ ∠QSR + 143° = 180°
➨ ∠QSR = 180° - 143°
➨ ∠QSR = 37°
∠PSR = ∠QSR + ∠y
➨90° = 37° + ∠y
➨∠y = 90° - 37°
➨∠y = 53°
∠x + ∠y + ∠SPQ = 180° [ Angle Sum Property of triangle ]
➨∠x + 53° + 90° = 180°
➨∠x + 143° = 180°
➨∠x = 180° - 143°
➨∠x = 37°
Therefore, x = 37° and y = 53°
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