In the figure, not drawn to scale. LMNP is a square. NPQ is an equilateral triangle and LN is a straight line. Find
- Two-thirds of ∠LRQ
- Five times of ∠QNR
(a)
∠PLN = 45° (Right angle)
∠RPN = 60° (Equilateral triangle)
∠LPR
= 90° - ∠RPN
= 90° - 60°
= 30°
∠LRQ
= 30° + 45° (Exterior angle of a triangle)
= 75°
Two-thirds of ∠LRQ
=
23 x 75°
= 50°
(b)
∠QRN
= 180° - ∠LRQ
= 180° - 75°
= 105° (Angles on a straight line)
∠QNR
= 180° - 60° - 105°
= 15° (Angles sum of triangle)
Five times of ∠QNR
= 5 x 15°
= 75°
Answer(s): (a) 50°; (b) 75°
