Advertisements
Advertisements
Question
The number of sides of a regular polygon whose each interior angle is of 135° is ______.
Options
6
7
8
9
Advertisements
Solution
The number of sides of a regular polygon whose each interior angle is of 135° is 8.
Explanation:
We know that, the measures of each exterior angle of a polygon having n sides is given by `360^circ/n`.
∴ The number of sides,
`n = 360^circ/"Exterior angle"`
= `360^circ/(180^circ - 135^circ)` ...[∵ Exterior angle + Interior angle = 180°]
= `360^circ/45^circ`
= 8
APPEARS IN
RELATED QUESTIONS
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
| Figure |  |
 |
 |
 |
| Side | 3 | 4 | 5 | 6 |
| Angle sum | 180° |
2 × 180° = (4 − 2) × 180° |
3 × 180° = (5 − 2) × 180° |
4 × 180° = (6 − 2) × 180° |
What can you say about the angle sum of a convex polygon with number of sides?
a) 7
b) 8
c) 10
d) n
Find the measure of each exterior angle of a regular polygon of 15 sides
Classify the following curve as open or closed:
State the name of a regular polygon of 4 sides.
Find the number of side of a regular polygon, when of its angle has a measure of 175° .
The sum of angles of a concave quadrilateral is ______.
The name of three-sided regular polygon is ______.
The number of diagonals in a hexagon is ______.
A regular polygon is a polygon whose all sides are equal and all ______ are equal.
is a polygon.
