In the figure, not drawn to scale. LMNP is a square. NPQ is an equilateral triangle and LN is a straight line. Find
- One-fifth of ∠LRQ
- Twice 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°
One-fifth of ∠LRQ
=
15 x 75°
= 15°
(b)
∠QRN
= 180° - ∠LRQ
= 180° - 75°
= 105° (Angles on a straight line)
∠QNR
= 180° - 60° - 105°
= 15° (Angles sum of triangle)
Twice of ∠QNR
= 2 x 15°
= 30°
Answer(s): (a) 15°; (b) 30°