In the figure, ∠LRV is a right-angled isosceles triangle. LV // NU , ∠TQP = 46°, ∠RTS = 41° and ∠PSQ = 57°. Find
- ∠LVR
- ∠QNU
- ∠SUT
(a)
∠LVR
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠RTM = 45° (Corresponding angles, VL//TM)
∠QTN
= ∠RTS + ∠RTM
= 41° + 45°
= 86°
∠QNU
= 180° - ∠TQP - ∠QTN
= 180° - 46° - 86°
= 48° (Angles sum of triangle)
(c)
∠STU
= 180° - ∠QTN
= 180° - 86°
= 94°(Angles in a straight line)
∠UST = ∠QSR = 57° (Vertically opposite angles)
∠SUT
= 180° - ∠UST - ∠STU
= 180° - 57° - 94°
= 29° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 48°; (c) 29°
