Question

given that the exterior angle of a regular hexagon is 2x,find the value of x,hence find the size of each interior angle of the hexagon​

Answer 1

x = 30 , interior angle = 120

Explanation:

the sum of the exterior angles of a polygon = 360°

since the hexagon is regular then exterior angles are congruent , then

6 × 2x = 360

12x = 360 ( divide both sides by 12 )

x = 30

then each exterior angle = 2x = 2 × 30 = 60°

the sum of exterior angle and interior angle = 180° , that is

interior angle + 60° = 180° ( subtract 60° from both sides )

interior angle = 120°