In the figure, ∠MSW is a right-angled isosceles triangle. MW // PV , ∠URQ = 46°, ∠SUT = 41° and ∠QTR = 56°. Find
- ∠MWS
- ∠RPV
- ∠TVU
(a)
∠MWS
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠SUN = 45° (Corresponding angles, WM//UN)
∠RUP
= ∠SUT + ∠SUN
= 41° + 45°
= 86°
∠RPV
= 180° - ∠URQ - ∠RUP
= 180° - 46° - 86°
= 48° (Angles sum of triangle)
(c)
∠TUV
= 180° - ∠RUP
= 180° - 86°
= 94°(Angles in a straight line)
∠VTU = ∠RTS = 56° (Vertically opposite angles)
∠TVU
= 180° - ∠VTU - ∠TUV
= 180° - 56° - 94°
= 30° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 48°; (c) 30°