In the figure, ∠NTX is a right-angled isosceles triangle. NX // QW , ∠VSR = 49°, ∠TVU = 38° and ∠RUS = 57°. Find
- ∠NXT
- ∠SQW
- ∠UWV
(a)
∠NXT
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠TVP = 45° (Corresponding angles, XN//VP)
∠SVQ
= ∠TVU + ∠TVP
= 38° + 45°
= 83°
∠SQW
= 180° - ∠VSR - ∠SVQ
= 180° - 49° - 83°
= 48° (Angles sum of triangle)
(c)
∠UVW
= 180° - ∠SVQ
= 180° - 83°
= 97°(Angles in a straight line)
∠WUV = ∠SUT = 57° (Vertically opposite angles)
∠UWV
= 180° - ∠WUV - ∠UVW
= 180° - 57° - 97°
= 26° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 48°; (c) 26°