In the figure, not drawn to scale. KLMN is a square. MNP is an equilateral triangle and KM is a straight line. Find
- Three-fifths of ∠KQP
- Nine times of ∠PMQ
(a)
∠NKM = 45° (Right angle)
∠QNM = 60° (Equilateral triangle)
∠KNQ
= 90° - ∠QNM
= 90° - 60°
= 30°
∠KQP
= 30° + 45° (Exterior angle of a triangle)
= 75°
Three-fifths of ∠KQP
=
35 x 75°
= 45°
(b)
∠PQM
= 180° - ∠KQP
= 180° - 75°
= 105° (Angles on a straight line)
∠PMQ
= 180° - 60° - 105°
= 15° (Angles sum of triangle)
Nine times of ∠PMQ
= 9 x 15°
= 135°
Answer(s): (a) 45°; (b) 135°
