In the figure, ∠JPT is a right-angled isosceles triangle. JT // LS , ∠RNM = 48°, ∠PRQ = 41° and ∠MQN = 55°. Find
- ∠JTP
- ∠NLS
- ∠QSR
(a)
∠JTP
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠PRK = 45° (Corresponding angles, TJ//RK)
∠NRL
= ∠PRQ + ∠PRK
= 41° + 45°
= 86°
∠NLS
= 180° - ∠RNM - ∠NRL
= 180° - 48° - 86°
= 46° (Angles sum of triangle)
(c)
∠QRS
= 180° - ∠NRL
= 180° - 86°
= 94°(Angles in a straight line)
∠SQR = ∠NQP = 55° (Vertically opposite angles)
∠QSR
= 180° - ∠SQR - ∠QRS
= 180° - 55° - 94°
= 31° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 46°; (c) 31°
