Question

In Fig. 6.43, if PQ ⊥ PS, PQ || SR, ∠ SQR = 28° and ∠ QRT = 65°, then find the valuesof x and y.

Answer 1

Answer:

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Given :-

• ∠ SQR = 28°

• ∠ QRT = 65°

To find

• Value of X and Y

Solution

∠ 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°