In the figure, TKLR is a trapezium and triangles TRP and PTN are isosceles triangles. SH, SL and HL are straight lines. TR = TP = PN. Find
- ∠s
- ∠t
(a)
∠KTN = 180° - ∠s (Interior angles, TK//SL)
∠PNT = 180° - ∠s (Angles on a straight line)
∠PTN = 180° - ∠s (Isosceles triangle)
49° + 180° - ∠s + 180° - ∠s + ∠t + 24° = 180° (Angles on a straight line, HS)
49° + 180° + 180° + 24° - ∠s - ∠s + ∠t = 180°
433° - 2∠s + ∠t = 180°
2∠s - ∠t = 433° - 180°
2∠s - ∠t = 253°
∠t = 2∠s - 253° --- (1)
∠TPR
= ∠TRP
= 2 x (180° - ∠s)
= 360° - 2∠s (Exterior angle of a triangle)
∠t = 180° - (360° - 2∠s) - (360° - 2∠s)
∠t = 180° - 360° + 2∠s - 360° + 2∠s
∠t = 180° - 360° - 360° + 2∠s + 2∠s
∠t = 4∠s - 540° (Angles sum of triangle)
∠t = 4∠s - 540° --- (2)
(2) = (1)
4∠s - 540° = 2∠s - 253°
4∠s - 2∠s= 540° - 253°
2∠s = 287°
∠s
= 287° ÷ 2
= 143.5°
(b)
From (1)
∠t
= 2∠s - 253°
= 287° - 253°
= 34°
Answer(s): (a) 143.5°; (b) 34°