CDEF is a square. VUE and DUF are straight lines. DC = DV and ∠UDV = 15°. Find
- ∠DCV
- ∠FEV
.
(a)
∠CDF = 45° (Right angle)
∠CDV
= ∠CDF - ∠UDV
= 45° - 15°
= 30°
∠DCV
= (180° - ∠CDV) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
DC = DV = DE
VDE is an isosceles triangle.
∠DVE = ∠DEV (Isosceles triangle)
∠DEV
= (180° - ∠FDE - ∠UDV) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠FEV
= ∠DEF - ∠DEV
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
