The number of sides of a regular polygon whose each interior angle is of 135° is
(a) 6
(b) 7
(c) 8
(d) 9

Solution:

Given, each interior angle of a regular polygon is 135°.

We have to find the number of sides of a regular polygon.

We know that the sum of interior angles of any polygon (convex or concave) having n sides is(n -2) x 180°.

Now, sum of interior angles = 135n

Now, 135° × n = (n - 2) × 180°

135n = 180n - 360

On solving for n,

180n - 135n = 360

45n = 360

n = 360/45

n = 40/5

n = 8

Therefore, the number of sides is 8.

✦ Try This: The number of sides of a regular polygon whose each interior angle is of 140° is

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 49

The number of sides of a regular polygon whose each interior angle is of 135° is (a) 6 (b) 7 (c) 8 (d) 9

Summary:

The number of sides of a regular polygon whose interior angle is 135° is 8.

☛ Related Questions:

• If a diagonal of a quadrilateral bisects both the angles, then it is a (a) kite (b) parallelogram (c . . . .
• To construct a unique parallelogram, the minimum number of measurements required is (a) 2 (b) 3 (c) . . . .
• To construct a unique rectangle, the minimum number of measurements required is (a) 4 (b) 3 (c) 2 (d . . . .