In the figure, ∠MSW is a right-angled isosceles triangle. MW // PV , ∠URQ = 50°, ∠SUT = 42° and ∠QTR = 58°. Find
- ∠MWS
- ∠RPV
- ∠TVU
(a)
∠MWS
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠SUN = 45° (Corresponding angles, WM//UN)
∠RUP
= ∠SUT + ∠SUN
= 42° + 45°
= 87°
∠RPV
= 180° - ∠URQ - ∠RUP
= 180° - 50° - 87°
= 43° (Angles sum of triangle)
(c)
∠TUV
= 180° - ∠RUP
= 180° - 87°
= 93°(Angles in a straight line)
∠VTU = ∠RTS = 58° (Vertically opposite angles)
∠TVU
= 180° - ∠VTU - ∠TUV
= 180° - 58° - 93°
= 29° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 43°; (c) 29°
