Question
Download Solution PDFIn quadrilateral PQRS, the bisectors of ∠R and ∠S meet at the point T (inside the quadrilateral) and ∠STR = 87.5°. If the ratio of ∠P to ∠Q is 2 ∶ 3, then what is the difference between the measures of ∠Q and ∠P?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
∠STR = 87.5°.
The bisectors of ∠R and ∠S meet at the point T
The ratio of ∠P to ∠Q is 2 ∶ 3
Calculation
∠P + ∠Q + ∠R + ∠S = 360
∠P + ∠Q = 360 - (∠R + ∠S) ..(1)
∠STR + ∠R/2 + ∠S/2 = 180
2∠STR = 360 - (∠R + ∠S) ..(2)
Put 2 in 1.
∠STR = (∠P + ∠Q)/2
∠P + ∠Q = 87.5 × 2 = 175°
(2 + 3) → 175°
1 → 175°/5 = 35°
The difference between the measures of ∠Q and ∠P is 35°.
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