STUV is a square. GFU and TFV are straight lines. TS = TG and ∠FTG = 13°. Find
- ∠TSG
- ∠VUG
.
(a)
∠STV = 45° (Right angle)
∠STG
= ∠STV - ∠FTG
= 45° - 13°
= 32°
∠TSG
= (180° - ∠STG) ÷ 2
= (180° - 32°) ÷ 2
= 148° ÷ 2
= 74° (Isosceles triangle)
(b)
TS = TG = TU
GTU is an isosceles triangle.
∠TGU = ∠TUG (Isosceles triangle)
∠TUG
= (180° - ∠VTU - ∠FTG) ÷ 2
= (180° - 45° -13°) ÷ 2
= 122° ÷ 2
= 61°
∠VUG
= ∠TUV - ∠TUG
= 90° - 61°
= 29°
Answer(s): (a) 74°; (b) 29°
