PSLETUVW is a parallelogram, TVX is an equilateral triangle and VW = WX.
- Find ∠TVW.
- Find ∠VWT.
- Find ∠XTU.
(a)
VW = WX
Triangle VWX is an isosceles triangle.
∠WVX
= (180° - 138°) ÷ 2
= 42° ÷ 2
= 21° (Isosceles triangle)
∠TVW
= 60° - 21°
= 39° (Equilateral triangle)
(b)
∠TXW
= 60° - 21°
= 39° (Equilateral triangle)
∠TWX
= 180° - 39° - 21°
= 120° (Angles sum of triangle)
∠TWV
= 360° - 138° - 120°
= 102° (Angles at a point)
∠UTV
= ∠TVW
= 39° (Alternate angles)
∠UTX
= 60° + 39°
= 99°
Answer(s): (a) 39°; (b) 102°; (c) 99°