Rehnuma makes different polygons using matchsticks and measure their interior angles with the help of a protractor. She makes a triangle with three matchsticks and adds one more to make a quadrilateral. Then she adds one more matchstick to make a pentagon and so on. Which of the following statements is correct about the angles of these shapes?

Question

Rehnuma makes different polygons using matchsticks and measure their interior angles with the help of a protractor. She makes a triangle with three matchsticks and adds one more to make a quadrilateral. Then she adds one more matchstick to make a pentagon and so on. Which of the following statements is correct about the angles of these shapes?

The sum of all the interior angles of any polygon is 360°.
The sum of all the interior angles of a quadrilateral is three times of the sum of all the interior angles of triangle.
When the numbers of side increases, the sum of the measures of interior angles of a polygon also increases.
When the numbers of sides increases sum of the measures of interior angles of a polygon also decreases.

LohaHridoy

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2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 3 : When the numbers of side increases, the sum of the measures of interior angles of a polygon also increases.

A Polygon is a flat or plane, 2-dimensional closed shape with straight sides. There are no curved sides to it. For example- triangle, quadrilateral, pentagon, hexagon, etc.

An Interior angle is an angle located inside a shape.

Interior angle property of a Polygon:

The sum of all the interior angles of a Polygon = (n-2) X 180º, where (n= number of sides).[ alt="polygon-1" src="//storage.googleapis.com/tb-img/production/22/05/polygon-1.png" style="width: 240px; height: 191px; float: right;">
For example- a triangle has 3 sides, and the sum of its interior angles will be (n-2)X180º = (3-2)X180º = 180º
A quadrilateral has 4 sides and the sum of its interior angles will be, (n-2)X180º = (4-2)X180º =360º
A Pentagon has 5 sides, and the sum of its interior angles will be (n-2)X180º =5-2X180º =540º

Hence, we conclude that when the number of sides increases, the sum of measures of interior angles of a polygon also increases by 180º.