In the figure, ∠JPT is a right-angled isosceles triangle. JT // LS , ∠RNM = 50°, ∠PRQ = 42° and ∠MQN = 61°. Find
- ∠JTP
- ∠NLS
- ∠QSR
(a)
∠JTP
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠PRK = 45° (Corresponding angles, TJ//RK)
∠NRL
= ∠PRQ + ∠PRK
= 42° + 45°
= 87°
∠NLS
= 180° - ∠RNM - ∠NRL
= 180° - 50° - 87°
= 43° (Angles sum of triangle)
(c)
∠QRS
= 180° - ∠NRL
= 180° - 87°
= 93°(Angles in a straight line)
∠SQR = ∠NQP = 61° (Vertically opposite angles)
∠QSR
= 180° - ∠SQR - ∠QRS
= 180° - 61° - 93°
= 26° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 43°; (c) 26°
