STUV is a square. LKU and TKV are straight lines. TS = TL and ∠KTL = 15°. Find
- ∠TSL
- ∠VUL
.
(a)
∠STV = 45° (Right angle)
∠STL
= ∠STV - ∠KTL
= 45° - 15°
= 30°
∠TSL
= (180° - ∠STL) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
TS = TL = TU
LTU is an isosceles triangle.
∠TLU = ∠TUL (Isosceles triangle)
∠TUL
= (180° - ∠VTU - ∠KTL) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠VUL
= ∠TUV - ∠TUL
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
