The figure is not drawn to scale. ∠QPR = 41°, QP = QR and PU//QT. Given that ∠x is
12 of ∠v and ∠x is 4 times of ∠w, find
- ∠x
- ∠t
(a)
x : v = 1 : 2
v = 2 x
w : x = 1 : 4
v = 2 x 4= 8
v : w : x = 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°
∠x
= 4 x 1 u
= 4 x 17°
= 68°
(b)
∠QRP = ∠QPR = 41° (Isosceles triangle)
∠RVT = ∠RPU = 68° (Corresponding angles, PU//QT)
∠t
= 68° - 41°
= 27° (Exterior angle of a triangle)
Answer(s): (a) 68°; (b) 27°
