Question

if each interior angle of a regular polygon is 135°,how many lines of symmetry will the polygon have?​

Answer 1

Given,

The value of each of the internal angles of a regular polygon = 135°

To find,

The number of lines of symmetry of that polygon.

Solution,

First of all, we have to calculate the number of sides of the given polygon by using the following mathematical formula.

Number of sides = 360°/(180°-value of internal angle)

= 360°/(180°-135°)

= 360°/45°

= 8

Now,

The number of lines of symmetry of a polygon = Number of sides of a polygon.

So, number of lines of symmetry of the given polygon = 8

Hence, the given polygon has 8 lines of symmetry.