STUV is a square. NMU and TMV are straight lines. TS = TN and ∠MTN = 11°. Find
- ∠TSN
- ∠VUN
.
(a)
∠STV = 45° (Right angle)
∠STN
= ∠STV - ∠MTN
= 45° - 11°
= 34°
∠TSN
= (180° - ∠STN) ÷ 2
= (180° - 34°) ÷ 2
= 146° ÷ 2
= 73° (Isosceles triangle)
(b)
TS = TN = TU
NTU is an isosceles triangle.
∠TNU = ∠TUN (Isosceles triangle)
∠TUN
= (180° - ∠VTU - ∠MTN) ÷ 2
= (180° - 45° -11°) ÷ 2
= 124° ÷ 2
= 62°
∠VUN
= ∠TUV - ∠TUN
= 90° - 62°
= 28°
Answer(s): (a) 73°; (b) 28°
