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What is the formula for finding exterior and interior angles of a polygon?

Answer 1

Mason Adams

Each interior angle of a regular polygon with #n# sides:

#color(red)(theta = (180(n-2))/n" or "theta = (180n-360)/n#

Each exterior angle of a regular polygon with #n# sides:

#color(green)(beta = 180°-theta#

Note that interior angle + exterior angle = #180°#

#theta = 180°-beta " and " beta = 180°-theta#

To find the size of each interior angle of a regular polygon you need to find the sum of the interior angles first.

If the number of sides is #n#, then

the sum of the interior angles is:

#color(blue)(S = 180(n-2))#

This formula derives from the fact that if you draw diagonals from one vertex in the polygon, the number of triangles formed will be #2# less than the number of sides. Each triangle has #180°#.

The formula can also be used as #color(blue)(S = 180n-360)#

This form of the formula derives from drawing triangles in the polygon by drawing lines from a central point to each vertex. In this way the number of triangles is the same as the number of sides, but the angles at the centre are not required, so #360°# is subtracted.

Once you have the sum of all the interior angles you divide by the number of sides to find

the size of each interior angle

#color(red)(theta = (180(n-2))/n)" or " color(red)(theta = (180n-360)/n)#

To find the size of each exterior angle, #beta#, subtract #theta# from #180°#

#color(green)(beta = 180°-theta#

Another method to find the exterior angle is using the fact that the sum of the exterior angles is always #360°#

#color(green)(beta = (360°)/n#

Once you know the size of the exterior angle you can find the size of the interior angle by subtracting from #180°#

#color(red)(theta = 180°-beta)#

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Answer 2

Sadie Allen

The formula for finding the sum of the exterior angles of a polygon is: (360^\circ).

The formula for finding the measure of each exterior angle of a regular polygon is: (\frac{360^\circ}{n}), where (n) is the number of sides.

The formula for finding the sum of the interior angles of a polygon is: ((n - 2) \times 180^\circ), where (n) is the number of sides.

To find the measure of each interior angle of a regular polygon, you can use the formula: (\frac{(n - 2) \times 180^\circ}{n}), where (n) is the number of sides.

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Answer from HIX Tutor

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