In the figure, YRSV is a trapezium and triangles YVU and UYT are isosceles triangles. XP, XS and PS are straight lines. YV = YU = UT. Find
- ∠f
- ∠g
(a)
∠RYT = 180° - ∠f (Interior angles, YR//XS)
∠UTY = 180° - ∠f (Angles on a straight line)
∠UYT = 180° - ∠f (Isosceles triangle)
56° + 180° - ∠f + 180° - ∠f + ∠g + 24° = 180° (Angles on a straight line, PX)
56° + 180° + 180° + 24° - ∠f - ∠f + ∠g = 180°
440° - 2∠f + ∠g = 180°
2∠f - ∠g = 440° - 180°
2∠f - ∠g = 260°
∠g = 2∠f - 260° --- (1)
∠YUV
= ∠YVU
= 2 x (180° - ∠f)
= 360° - 2∠f (Exterior angle of a triangle)
∠g = 180° - (360° - 2∠f) - (360° - 2∠f)
∠g = 180° - 360° + 2∠f - 360° + 2∠f
∠g = 180° - 360° - 360° + 2∠f + 2∠f
∠g = 4∠f - 540° (Angles sum of triangle)
∠g = 4∠f - 540° --- (2)
(2) = (1)
4∠f - 540° = 2∠f - 260°
4∠f - 2∠f= 540° - 260°
2∠f = 280°
∠f
= 280° ÷ 2
= 140°
(b)
From (1)
∠g
= 2∠f - 260°
= 280° - 260°
= 20°
Answer(s): (a) 140°; (b) 20°