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The 3 interior angles of this equilateral triangle will add up to 180 degrees

Q: What is the sum of the measures of the interior angles of a polygon if each exterior angle measures 120 degrees?

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Each exterior angle measures 11.5 degrees. Each interior angle measures 168.75 degrees

There are 5 interior angles and each one measures 108 degrees (180-72). Since the sum of exterior angles of any polygon is 360⁰, then that polygon would have 5 angles (360/72). So the sum of interior angle measures is 540⁰.

Sum of exterior angles = 360 degrees Sum of interior angles = 1980 degrees

A regular polygon with interior angles measuring 165 degrees each will have exterior angles measuring 15 degrees each, since each pair of interior/exterior angles forms a linear pair whose measures total 180 degrees. For any polygon, the sum of the exterior angles is 360 degrees. You can find how many sides, and therefore vertices, in the polygon by dividing 360 by 15. In this case, the polygon has 360/15 = 24 sides.

A regular polygon has sides of equal length, as well as interior angles of equal measure. But for any regular polygon, the sum of the measures of the exterior angles is 360 degrees. You can use this information to find out the measure of an interior angle, because the sum of the measures of each interior/exterior pair of angles is always 180 degrees. So to find the answer to this problem, divide 360 by 7. Each exterior angle is about 51.4 degrees. Subtract that number from 180. Each interior angle is about 128.6 degrees.

Related questions

1800 degrees

1440 degrees

1440 degrees

Interior angle = 120 degrees Exterior angle = 60 degrees

Each exterior angle measures 20 degrees Each interior angle measures 160 degrees

540 degrees

The sum of a regular polygon's interior angles is always equal to (n-2) * 180, where n is the number of sides in the polygon. Given that one exterior angle measures 40 degrees, we can find the interior angle by subtracting 40 from 180 degrees (since the exterior and interior angles are supplementary) to get 140 degrees. So, the sum of the interior angles of the regular polygon is 140 * n.

The interior angle of any regular polygon can be calculated using the formula 180 * (n - 2) / n, where n is the number of sides. In this case, since each exterior angle measures 72 degrees, the interior angle would be 180 - 72 = 108 degrees. So the measures of the interior angles in this regular polygon would be 108 degrees.

30 degrees

150 degrees.

1440 degrees

540 degrees