Sum of the Measures of Angles of a Polygon

IMPORTANT

Sum of the Measures of Angles of a Polygon: Overview

From this topic, we will talk about the sum of the measures of angles of a polygon. We will learn the different formulae related to angles. It discusses the sum of interior and exterior of polygons of 'n' sides.

Important Questions on Sum of the Measures of Angles of a Polygon

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Find the measure of interior angle of a regular octagon in degrees.

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Find the sum of Interior angles of a polygon of 47 sides.

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Find the sum of Interior angles of a polygon of 22 sides.

EASY
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Find the sum of Interior angles of a polygon of 7sides

EASY
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Find the sum of Interior angles of a polygon of 15 sides.

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Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

Figure Question Image Question Image Question Image Question Image
Side 3 4 5 6
Angle
180°

2×180°
=(4-2)×180°

3×180°
=(5-2)×180°

4×180°
=(6-2)×180°

If the angle sum of a convex polygon with the number of sides equal to 7 is k°, then find the value of k.

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In the figure given above PQRS is a quadrilateral. What is the measure of $ \angle $PSR ?

MEDIUM
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The angles of a quadrilateral are $ {x°}$, $ {(x-20)}^{°}$, $ {(x-30)}^{°}$, and $ 2{x°}$. What is the value of the greatest angle?

EASY
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The two angles of a quadrilateral are equal to $ 78°$ and $ 142°$ and the other two angles are equal. The measure of the equal angles are

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What is the value of ∠$ S$ ?

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ABCD and PQRS are 2 quadrilaterals. Choose the correct statement from the following.

EASY
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The sum of the angles of a quadrilateral is

EASY
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The sum of the angles of a quadrilateral is equal to the sum of

EASY
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Sarita when solving some problems on polygons found that sum of all its interior angles is $ 2753$$ °$. Is Sarita correct?

MEDIUM
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If each interior angle of a regular polygon of 24 sides is k°, then find the value of k.

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The value of x in the figure is:

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Find the measure of each interior angle if the polygon is a decagon.

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In a quadrilateral ABCDA+C is 2 times B+D. If A=140° and D=60°, then B= 

EASY
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The angles of a quadrilateral are x°,x-10°,x+30° and 2x°, the smallest angle is equal to 

MEDIUM
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The angles of a quadrilateral are in the ratio 1:2:3:4. The largest angle is