Question
Download Solution PDFIn Δ PQR, S is the mid-point of QR and PS = SR. If ∠Q = 48°, then what will be the measure (in degrees) of ∠SPR?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven :
S is the mid point.
And PS = SR
∠Q = 48°
Calculation :
Since, SR = PS and QS = SR
So, PS = SR = QS
In ΔPQS,
∠Q = 48° , ∠P = 48°
⇒ ∠Q + ∠P + ∠S = 180°
⇒ ∠S = 180° - 96° = 84°
Now, ∠QSP + ∠PSR = 180°
⇒ 84° + ∠PSR = 180°
⇒ ∠PSR = 180° - 84° = 96°
In ΔPSR,
⇒ ∠P + ∠S + ∠R = 180°
⇒ 96° + x + x = 180°
⇒ 2x = 180° - 96° = 84°
⇒ x = 42°
∠SPR = 42°
∴ The correct answer is 42°.
Last updated on May 9, 2025
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