Sum of the Measures of the Exterior Angles of a Polygon

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Sum of the Measures of the Exterior Angles of a Polygon: Overview

This topic states that the sum of the measures of the external angles of any polygon is 360 degrees. We can find a number of sides of a regular polygon with the given angle. We can find the number of the sides by dividing the exterior with 360 degrees.

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

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K° is the maximum exterior angle possible for a regular polygon, then find the value of k.

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

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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 ?

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An outline of a camping tent is shown below. The value of $ x$ is_____ degrees.

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The value of x is_____ degrees.

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Two regular polygons are joined as shown below, The value of x is_____ degrees.

 

(Round your answer to the nearest degree.)

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The border of a coin is in the shape of regular polygon. The measure of each interior angle of the border is_____ degrees.

(Round your answer to the nearest degree.)

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The sum of the interior angle in a regular polygon is$ 1260°$. The measure of one of the interior angles of the polygon is_____$ °$.

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Find the sum of the interior angle measures of a 13-gon.

Ram and Shyam solve the above question in their unit test. The solutions they write are given below. Which solution is correct?

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For the polygon shown below, the value of $ x$ is _____$ °$ .

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The sum of the interior angle measures of the spider web shown below is_____ degrees.

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The sum of the interior angle measures of the school crossing sign is_____ degrees.

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Some lines are intersecting each other to form a polygon. Some of the angles are marked with numbers. Ram identifies these angles as internal angles of the polygon.

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Does Ram identify these angles correctly?

 

 

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I am a regular polygon with one exterior angle of 20 degrees. The sum of my interior angles is_____$ °$.

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A regular polygon has one exterior angle measuring 1°, therefore the number of sides of the polygon is_____.

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In the figure below, the measure of ∠$ \text{a}$=_____$ \text{°}$.

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What is the sum of the measure of the exterior angles of a decagon?

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If the measure of interior angles of a convex pentagon are five consecutive numbers, the measure of its largest interior angle is_____ degrees.

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The interior angle measures of a convex pentagon are consecutive multiples of 4. The measure of its smallest interior angle is_____ degrees.

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The sum of the interior angles of a regular polygon is 2700$ °$ . Therefore, the number of sides of the polygon is _____.