Question

AB,BC,CD are three consecutive sides of a regular polygon.If angle BAC=20°,find: (i)its each interior angle (ii) its each exterior angle (iii)the number of sides in the polygon

Answer 1

AB,BC,CD are three consecutive sides of a regular polygon
so, regular polygon always have equal sides
AB = BC

in triangle ABC

if two sides are equal then opposite angle for the two sides are also equal

then, angle BAC = angle BCA

given, angle BAC=20°
so, angle BCA = 20°

angle BAC + angle BCA + angle ABC = 180°
20° + 20° + angle ABC = 180°
angle ABC = 180° - 40°
angle ABC = 140°

(i)its each interior angle, angle ABC = 140°

(ii) its each exterior angle = 180° - 140° = 40°

(iii)the number of sides in the polygon = (360°/40°) = 9