Answer:
The number of sides of the polygon with 135° interior angle is 8
Step-by-step explanation:
Given as :
The measure of each interior angle of regular polygon = 135°
Let The total number of sides = n
So, each internal angle of a regular polygon with n sides = [tex]180^{\circ}- \frac{360^{\circ}}{n}[/tex]
or, 135° = [tex]180^{\circ}- \frac{360^{\circ}}{n}[/tex]
or, [tex]\frac{360^{\circ}}{n}[/tex] = 180° - 135°
or, [tex]\frac{360^{\circ}}{n}[/tex] = 45°
∴ n = [tex]\frac{360^{\circ}}{45^{\circ}}[/tex]
I.e n = 8
Hence the number of sides of the polygon with 135° interior angle is 8 Answer
