In the figure, not drawn to scale. JKLM is a square. LMN is an equilateral triangle and JL is a straight line. Find
- One-fifth of ∠JPN
- Five times of ∠NLP
(a)
∠MJL = 45° (Right angle)
∠PML = 60° (Equilateral triangle)
∠JMP
= 90° - ∠PML
= 90° - 60°
= 30°
∠JPN
= 30° + 45° (Exterior angle of a triangle)
= 75°
One-fifth of ∠JPN
=
15 x 75°
= 15°
(b)
∠NPL
= 180° - ∠JPN
= 180° - 75°
= 105° (Angles on a straight line)
∠NLP
= 180° - 60° - 105°
= 15° (Angles sum of triangle)
Five times of ∠NLP
= 5 x 15°
= 75°
Answer(s): (a) 15°; (b) 75°