In △PQR, ∠Q = 84º, ∠R = 48º, PS Ʇ QR at S and the bisector of ∠P meets QR at T. What is the measure of ∠SPT?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 18º
Concept
In ΔPQR
∠QPR + ∠Q + ∠R = 180°
∠QPR + 84° + 48° = 180°
∠QPR = 180° - 132°
∠QPR = 48°
∠QPT = 48°/2
∠ QPT = 24°
In ΔQPT
∠QPT + ∠PQT + ∠PTQ = 180°
Putting the value of ∠ QPT = 24°
24° + 84° + ∠PTQ = 180°
∠PTQ = 180° - 108°
∠PTQ = 72°
According to the question
In ΔPST
∠PST + ∠PTS + ∠SPT = 180°
Putting the value of ∠PTQ = 72°
90° + 72° + ∠SPT = 180°
∠SPT = 180° - 162°
∠SPT = 18°
Alternate Solution
∠SPT = (∠Q - ∠R) / 2
Putting the values
∠SPT = (84 - 48) / 2
= 36 / 2
= 18°