In the figure, ∠LRV is a right-angled isosceles triangle. LV // NU , ∠TQP = 46°, ∠RTS = 38° 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
= 38° + 45°
= 83°
∠QNU
= 180° - ∠TQP - ∠QTN
= 180° - 46° - 83°
= 51° (Angles sum of triangle)
(c)
∠STU
= 180° - ∠QTN
= 180° - 83°
= 97°(Angles in a straight line)
∠UST = ∠QSR = 57° (Vertically opposite angles)
∠SUT
= 180° - ∠UST - ∠STU
= 180° - 57° - 97°
= 26° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 51°; (c) 26°