The figure is not drawn to scale. ∠QPR = 41°, QP = QR and PU//QT. Given that ∠s is
12 of ∠q and ∠s is 4 times of ∠r, find
- ∠s
- ∠p
(a)
s : q = 1 : 2
q = 2 s
r : s = 1 : 4
q = 2 x 4= 8
q : r : s = 8 : 1 : 4
∠QRP = 41° (Isosceles triangle)
∠PRS
= 180° - 41°
= 139° (Angles on a straight line)
1 u + 4 u + 8 u + 139° = 360° (Sum of angles in a quadrilateral)
13 u = 360° - 139° = 221°
1 u = 221 ÷ 13 = 17°
∠s
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠QRP = ∠QPR = 41° (Isosceles triangle)
∠RVT = ∠RPU = 68° (Corresponding angles, PU//QT)
∠p
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°
