Question

Find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of the given regular polygon.14.Hexagon15.Square16.Octagon17.Pentagon18.15-gon19.20-gonEach regular polygon has radii and apothem as shown. Find the measure of each numbered angle.

Answer 1

Answer:

Step-by-step explanation:

Let radius = r and side of a regular polygon = s

a) The consecutive radii = r + r + 1

i) For Square ( 4- sides) : r + r + 1 = 90°

2r + 1 = 90°

ii) For Pentagon (5- sides) :  2r + 1 =108°

iii) For Hexagon (6- sides): 2r + 1 = 120°

iv) For Heptagon (7- sides): 2r + 1 = 129°

v) For Octagon (8- sides): 2r + 1 = 135°

vi) For Nonagon (9- sides): 2r + 1 = 140°

vii) For 20 sides: 2r + 1 = 162°

b) A radius and a side = r + s

i) For Square (4- sides): r + s = 90°

ii ) For Pentagon (5- sides): r + s = 108°

iii) For Hexagon (6- sides): r + s = 120°

iv) For Heptagon (7- sides): r + s = 129°

v) For Octagon (8- sides): r + s = 135°

vi) For Nonagon (9- sides): r + s = 140°

vii) For 20 sides: r + s = 162°