Question

Two sides of a regular pentagon are produced to form angle x. what is x

Answer 1

Given a regular pentagon,

Two sides of the pentagon are produced to form angle x.

Therefore, x is an interior angle

              

We know that the Sum of exterior angles of a pentagon = 360°

In a regular pentagon, all angles are equal,

Therefore, each exterior angle of a regular pentagon = 360/5 = 72 degrees

 

We also know that an exterior angle and its corresponding interior angle are supplements.

Therefore, each interior angle of a regular pentagon = 180 – 72 = 108 degrees

 

Therefore, x = 108 degrees