(a) A pentagon is such that one of its exterior sides is 60°. Two others are (90 – m)° each while the remaining angles are (30 + 2m)° each. Find the value of m.
(b)
In the diagram, PQR is a straight line, (overline{QR} = sqrt{3} cm) and (overline{SQ} = 2 cm). Calculate, correct to one decimal place, < PQS.
Explanation
The sum of exterior angles = 360°
(60° + 2(90 – m)° + 2(30 + 2m)° = 360°)
(60° + 180° – 2m° + 60° + 4m° = 360°)
(300° + 2m = 360°)
(implies 2m = 360° – 300° = 60°)
(m = 30°)
(b)
In (Delta QRS, cos Q = frac{sqrt{3}}{2})
(cos Q = 0.8660 implies Q = 30°)
(therefore < SQR = 30°^)
(< PQS = 180° – 30° ) (angles on a straight line = 180°)
(< PQS = 150°)