In the figure, ∠LRV is a right-angled isosceles triangle. LV // NU , ∠TQP = 50°, ∠RTS = 43° and ∠PSQ = 54°. Find
- ∠LVR
- ∠QNU
- ∠SUT
(a)
∠LVR
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠RTM = 45° (Corresponding angles, VL//TM)
∠QTN
= ∠RTS + ∠RTM
= 43° + 45°
= 88°
∠QNU
= 180° - ∠TQP - ∠QTN
= 180° - 50° - 88°
= 42° (Angles sum of triangle)
(c)
∠STU
= 180° - ∠QTN
= 180° - 88°
= 92°(Angles in a straight line)
∠UST = ∠QSR = 54° (Vertically opposite angles)
∠SUT
= 180° - ∠UST - ∠STU
= 180° - 54° - 92°
= 34° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 42°; (c) 34°