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in the adjoining figure PQ is equals to RP and angle QPR= 40 degree and angle PQS= 30 degree prove that QR is equals to QS ​

in the adjoining figure PQ is equals to RP and angle QPR 40 degree and angle PQS 30 degree prove that QR is equals to QS class=

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Answer:

Angle PSQ measures 180° - (30° + 40°) = 180° - 70° = 110°, so angle QSR measures 70°.

∆PQR is an isosceles triangle, so angles PQR and PRQ measure (180° - 40°)/2 = 140°/2 = 70°. Angle SRQ also measures 70°.

Angle SQR measures 70° - 30° = 40°.

From this, we conclude that ∆QRS is an isosceles triangle with QR = QS.

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