If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon. State whether the statement is true or false.
Solution:
Given, If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon.
We have to determine if the given statement is true or false.
A hexagon is defined as a closed 2D shape that is made up of six straight lines.
It is a two-dimensional shape with six sides, six vertices, and six interior angles.
We know that the sum of interior angles of a polygon is (n - 2) × 180°,
where n is the number of sides of the polygon.
Here, n = 6
Sum of angles = (6 - 2) × 180°
= 4 × 180°
= 720°
The sum of interior angles of a hexagon is 720°.
We know that the sum of exterior angles of a polygon is 360°.
Now, sum of interior angle = 2(sum of exterior angle)
= 2(360°)
= 720°
Therefore, the sum of interior angles is double the sum of exterior angles in a hexagon.
✦ Try This: If the sum of interior angles is equal to the sum of exterior angles taken in an order of a polygon, then it is a parallelogram. State whether the statement is true or false.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 103
If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon. State whether the statement is true or false.
Summary:
The given statement, ”If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon” is true
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