In the figure, ∠NTX is a right-angled isosceles triangle. NX // QW , ∠VSR = 51°, ∠TVU = 42° and ∠RUS = 53°. Find
- ∠NXT
- ∠SQW
- ∠UWV
(a)
∠NXT
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠TVP = 45° (Corresponding angles, XN//VP)
∠SVQ
= ∠TVU + ∠TVP
= 42° + 45°
= 87°
∠SQW
= 180° - ∠VSR - ∠SVQ
= 180° - 51° - 87°
= 42° (Angles sum of triangle)
(c)
∠UVW
= 180° - ∠SVQ
= 180° - 87°
= 93°(Angles in a straight line)
∠WUV = ∠SUT = 53° (Vertically opposite angles)
∠UWV
= 180° - ∠WUV - ∠UVW
= 180° - 53° - 93°
= 34° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 42°; (c) 34°
