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
- ∠g
- ∠h
(a)
∠RYT = 180° - ∠g (Interior angles, YR//XS)
∠UTY = 180° - ∠g (Angles on a straight line)
∠UYT = 180° - ∠g (Isosceles triangle)
49° + 180° - ∠g + 180° - ∠g + ∠h + 19° = 180° (Angles on a straight line, PX)
49° + 180° + 180° + 19° - ∠g - ∠g + ∠h = 180°
428° - 2∠g + ∠h = 180°
2∠g - ∠h = 428° - 180°
2∠g - ∠h = 248°
∠h = 2∠g - 248° --- (1)
∠YUV
= ∠YVU
= 2 x (180° - ∠g)
= 360° - 2∠g (Exterior angle of a triangle)
∠h = 180° - (360° - 2∠g) - (360° - 2∠g)
∠h = 180° - 360° + 2∠g - 360° + 2∠g
∠h = 180° - 360° - 360° + 2∠g + 2∠g
∠h = 4∠g - 540° (Angles sum of triangle)
∠h = 4∠g - 540° --- (2)
(2) = (1)
4∠g - 540° = 2∠g - 248°
4∠g - 2∠g= 540° - 248°
2∠g = 292°
∠g
= 292° ÷ 2
= 146°
(b)
From (1)
∠h
= 2∠g - 248°
= 292° - 248°
= 44°
Answer(s): (a) 146°; (b) 44°