How To Find The Measure Of One Exterior Angle

Unit of measurement xv Section 2 : Bending Backdrop of Polygons

In this department we calculate the size of the interior and exterior angles for different regular polygons.
In a regular polygon the sides are yet length and the interior angles are all the same size.

The post-obit diagram shows a regular hexagon:

Note that, for any point in a polygon, the interior angle and outside angle are on a straight line and therefore add up to 180°.
This ways that we tin work out the interior angle from the exterior bending and vice versa:

Interior Angle = 180° – Outside Angle

Exterior Angle = 180° – Interior Angle

If yous follow around the perimeter of the polygon, turning at each exterior angle, y'all do a consummate turn of 360°.

In every polygon, the outside angles always add up to 360°

Since the interior angles of a regular polygon are all the aforementioned size, the exterior angles must also be equal to 1 some other.
To find the size of one outside angle, we merely have to divide 360° past the number of sides in the polygon.

In a regular polygon, the size of each exterior bending = 360° ÷ number of sides
In this instance, the size of the exterior angle of a regular hexagon is 60° because
360° ÷ 6 = 60° and the interior angle must be 120° because 180° – 60° = 120°

This also ways that we can find the number of sides in a regular polygon if we know the exterior bending.

In a regular polygon, the number of sides = 360° ÷ size of the exterior angle

We tin can use all the above facts to work out the answers to questions virtually the angles in regular polygons.

Example Question 1
A regular octagon has viii equal sides and eight equal angles.

(a) Calculate the size of each exterior angle in the regular octagon.
We do this by dividing 360° past the number of sides, which is viii.
The answer is 360° ÷ eight = 45°.

(b) Calculate the size of each interior angle in the regular octagon.
We do this by subtracting the size of each exterior angle, which is 45°, from 180°.
The reply is 180° – 45° = 135°.

Example Question 2
A regular polygon has equal exterior angles of 72°.

(a) Summate the size of each interior angle in the regular polygon.
We do this by subtracting the exterior angle of 72° from 180°.
The answer is 180° – 72° = 108°.

(b) Summate the number of sides in the regular polygon.
We exercise this by dividing 360° past the size of i exterior bending, which is 72°.
The answer is 360° ÷ 72° = 5 sides.

Practice Question
Work out the answers to this question then click on the buttons marked to see whether you are correct.

The interior angles of a regular polygon are all equal to 140°.

(a) What is the size of each of the exterior angles in the regular polygon?

(b) How many sides does the polygon have?

(c) What is the proper noun of the polygon?

Source: https://www.cimt.org.uk/projects/mepres/book8/bk8i15/bk8_15i2.htm#:~:text=Since%20the%20interior%20angles%20of,of%20sides%20in%20the%20polygon.

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