Q&A for How to Calculate the Sum of Interior Angles

Work out what all the interior adds up to, then divide by however many sides the shape has.

Divide that sum by 180°, then add 2. In this example, 1080° / 180° = 6. 6 + 2 = 8. The polygon has 8 sides.

In the rhombus you describe, the two smaller interior angles would each be 60°, and the two larger interior angles would each be 120°. You wouldn't have to calculate the angles. Simple inspection of the rhombus and the two triangles would show what the angles are, given that equilateral triangles have three 60° angles. The sum is 60° + 60° + 120° + 120°.

Not necessarily. A triangle's sum is 180, a quadrilateral's sum is 360, and a pentagon's sum is 540. These are all polygons. Use the formula 180(n-2) where "n" is the number of the sides of the polygon in question to find your sum.

The formula for finding the sum of the interior angles of a polygon is the same, whether the polygon is regular or irregular. So you would use the formula (n-2) x 180, where n is the number of sides in the polygon.

First calculate the sum of all the interior angles of the polygon by using the formula (n - 2)(180°), where n is the number of sides. Then add together all of the known angles, and subtract that sum from the sum you calculated first. That will give you the missing angle.

The sum of the angles in a triangle is 180°. The sum of the angles in a square (or other quadrilateral) is 360 °. Since two congruent triangles will combine to form a square or other quadrilateral, the sum of the angles in one of the triangles is half of 360°, or 180°.

To find the interior angle, subtract the exterior angle from 180°.

Without a protractor you would have to know all of the linear dimensions of the polygon, divide the figure into various right triangles, and then use trigonometric functions to find the interior angles. In other words, it would be better to use a protractor on an irregular polygon.

By counting them manually. Drawing a diagram is usually the easiest way to visualize this as described in Method 2 above.

If you draw a diagonal within a square, it forms two triangles. If you draw both diagonals in a square, they form four triangles.

It's the angle outside the polygon between one side and the extension of the adjacent side.

You can use this to measure the angles. That is why it is needed in school for geometry.

Lacking further information, the only way to do that is with a protractor.

There are no polygons with intersecting sides because that would simply be two separate shapes. However, if there were, then yes, it would work.

A regular polygon with interior angles of 179° is practically a circle. In other words, it has a lot of (short) sides! The number of sides is found this way: the exterior angles of a regular polygon add up to 360°. All of the exterior angles in this case are 1° (180° - 179°). That means there are 360 exterior angles, 360 interior angles, 360 vertices, and therefore 360 sides.

Regarding regular polygons, the sum of the exterior angles is 360°. Divide 360° by one exterior angle. That will equal the number of exterior angles as well as the number of sides.

Yes. (4 - 2)(180°) = (2)(180°) = 360°.

A rectangle has four sides and four angles. Each angle is 90°. (4)(90°) = 360°. To use the formula given above, Sum = (n - 2)(180°) = (4 - 2)(180°) = (2)(180°) = 360°.

A heptagon has seven sides.The sum of its angles is (7 - 2)(180°) = (5)(180°) = 900°.

Like a regular pentagon, an irregular pentagon has interior angles that total 540°.

Yes. Sum = (6-2)(180°) = (4)(180°) = 720°.

The sum of the measures of the interior angles of convex n -gon is (n-2)*180.

Knowing those side lengths does not tell you anything about the angles.

The sum of the interior angles of any hexagon is 720°. So 720 = 107 + 2x + 150 + 95 + (2x - 15) + 123 = 4x + 460. Then 260 = 4x, and x = 65.

if you are given the exterior angle, you subtract it from 180 and you get the interior angle.

if you know the sum, just divide it by the number of sides of the polygon.

A cube has six sides, and each side has four 90° angles. So each side has a total of 360° in interior angles, and the cube has a total of 6 x 360° = 2160° in interior angles.

We must first assume that it's a regular polygon. If the external angle is 72°, each internal angle is 180° - 72° = 108°. A regular polygon with angles of 108° each is a pentagon (five sides).

360 degrees minus the interior angle will give you the exterior angle.