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

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How do I find a single interior angle?

Community Answer

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

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Question

How do I calculate the number of sides of a polygon if the sum of the interior angles is 1080?

Donagan

Top Answerer

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

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If two equilateral triangles are placed together to form a rhombus, how do I calculate the value of each interior angle of this rhombus, and how do I find the sum?

Donagan

Top Answerer

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°.

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Does a regular polygon's interior angles add up to 160?

Community Answer

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.

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Question

How do I find the sum of the interior angles of an irregular polygon?

Community Answer

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.

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How do I find the missing angle of an irregular polygon?

Donagan

Top Answerer

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.

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Why is the sum of an interior angle 180?

Community Answer

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°.

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Question

If the exterior angle is 72, what is the interior angle?

Donagan

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

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How can we work out 1 or more interior angles of an irregular polygon without a protractor?

Donagan

Top Answerer

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.

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How do I find the number of triangles in a polygon?

Community Answer

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

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How many triangles are in a square?

Donagan

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

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Question

What is the exterior angle of a polygon?

Donagan

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

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What do I use a protractor for?

Community Answer

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

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How do I find one interior angle in an irregular polygon?

Donagan

Top Answerer

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

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Would this equation work for polygons with intersecting sides?

Community Answer

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

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Question

How do I find the number of sides of a polygon with the interior angle of 179?

Donagan

Top Answerer

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.

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Question

How do I find the number of sides from the exterior angle?

Donagan

Top Answerer

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.

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Is the sum of the interior angles in a rectangle sum=4-2x180?

Community Answer

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

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Question

If you have a rectangle, how do you get the sum of the interior angles?

Donagan

Top Answerer

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°.

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How do I calculate the sum of interior angle of a heptagon?

Donagan

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

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What is the sum of the interior angles of an irregular pentagon?

Donagan

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

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Is the sum of a hexagon's interior angles equal to 720°?

Donagan

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

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Is this formula applicable for a convex polygon?

Abigai Osei Ayebi

Community Answer

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

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Question

How do I find the angles of a parallelogram if 2 sides are 184.15mm and the other 2 sides are 260.35mm?

Donagan

Top Answerer

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

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If interior angles of an hexagon are 107,2x°,150°,95°,(2x-15)° and 123°, what is x?

Donagan

Top Answerer

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.

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Question

How do I measure a single interior angle?

Community Answer

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

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Question

How do I find the number of each angle if I know the sum of the measure of the interior angle?

Community Answer

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

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Question

How do I calculate the sum of interior angles of a cube?

Donagan

Top Answerer

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.

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If the external angle is 72, then how many sides does the polygon have?

Donagan

Top Answerer

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).

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Question

How do I work out the exterior angle?

Community Answer

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

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