In the figure, RS is a straight line. ∠QTR = 90°, ∠UTV is equal to ∠VTS but 30° more than ∠QTU.
- What line is perpendicular to RS?
- Find ∠UTV.
(a)
Line QT or TQ is perpendicular to RS
(b)
∠UTV = ∠VTS = 1 u
∠QTU = 1 u - 30°
1 u + 1 u + 1 u - 30° = 90° (Right angle)
3 u = 90° + 30° = 120°
1 u = 120° ÷ 3 = 40°
Answer(s): (a) QT or TQ; (b) 40°