Interior Angles with Regular Polygons

Interior Angles - How it Works - Video

Example 1

Example 1:

Any quadrilateral has 2 triangles when we draw diagonals from one vertex to all the others. Remember each triangle has 180°. In the case in the picture on the left, we have two triangles each having a total of 180°. The sum of both triangles ==> 180° + 180° or 180° * 2 = 360°. The 360° represents the total amount of degrees inside the polygon. To find the measurement of the each angle inside, the quadrilateral must be a rectangle or a square.

We can use the formula 180° - 360°/n, where n is the number of sides, to find the measurement of each interior angle.

Now we have 180° - 360°/4 ==> 180° - 90° ==> 90°. So each angle on the side of the regular quadrilateral is 90°.

Example 2

Example 2:

Any pentagon has 3 triangles when we draw diagonals from one vertex to all the others. Remember each triangle has 180°. In the case in the picture on the left, we have three triangles each having a total of 180°. The sum of both triangles ==> 180° * 3 = 540°. The 540° represents the total amount of degrees inside the polygon. To find the measurement of the each angle inside, the pentagon must be regular or all the sides are the same.

We can use the formula 180° - 360°/n, where n is the number of sides, to find the measure of each interior angle.

Now we have 180° - 360°/5 ==> 180° - 72° ==> 108°. So each angle on the side of the regular quadrilateral is 108°.

Example 3

Example 3:

Any hexagon has 4 triangles when we draw diagonals from one vertex to all the others. Remember each triangle has 180°. In the case in the picture on the left, we have three triangles each having a total of 180°. The sum of both triangles ==> 180° * 4 = 720°. The 720° represents the total amount of degrees inside the polygon. To find the measurement of the each angle inside, the pentagon must be regular or all the sides are the same.

We can use the formula 180° - 360°/n, where n is the number of sides, to find the measure of each interior angle.

Now we have 180° - 360°/6 ==> 180° - 60° ==> 120°. So each angle on the side of the regular quadrilateral is 120°.

Example 4

Example 4:

Any heptagon has 5 triangles when we draw diagonals from one vertex to all the others. Remember each triangle has 180°. In the case in the picture on the left, we have three triangles each having a total of 180°. The sum of both triangles ==> 180° * 5 = 900°. The 900° represents the total amount of degrees inside the polygon. To find the measurement of the each angle inside, the pentagon must be regular or all the sides are the same.

We can use the formula 180° - 360°/n, where n is the number of sides, to find the measure of each interior angle.

Now we have 180° - 360°/7 ==> 180° - 51 and 3/7° ==> 128 and 4/7°. So each angle on the side of the regular quadrilateral is 128 and 4/7°.

Example 5

Example 5:

Any octagon has 6 triangles when we draw diagonals from one vertex to all the others. Remember each triangle has 180°. In the case in the picture on the left, we have three triangles each having a total of 180°. The sum of both triangles ==> 180° * 6 = 720°. The 720° represents the total amount of degrees inside the polygon. To find the measurement of the each angle inside, the pentagon must be regular or all the sides are the same.

We can use the formula 180° - 360°/n, where n is the number of sides, to find the measure of each interior angle.

Now we have 180° - 360°/6 ==> 180° - 60° ==> 120°. So each angle on the side of the regular quadrilateral is 120°.

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