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

Question

Mason Adams · Accepted Answer

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)#

Sadie Allen · Answer

undefined 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.