Angles Of Polygons Coloring Activity Answer Key Pdf (2024)

FAQs

What is the sum of the measures of the interior angles of a 23 gon? ›

∴ , the sum of the interior angles is 3780∘ .

The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.

To find the interior angle sum of a polygon, we can use a formula: interior angle sum = (n - 2) x 180°, where n is the number of sides. For example, a pentagon has 5 sides, so its interior angle sum is (5 - 2) x 180° = 3 x 180° = 540°. Created by Sal Khan.

The sum of the exterior angles of a polygon is 360°. Calculation: As each exterior angle of a regular polygon is 18°. ∴ The number of sides of the polygon is 20 when each exterior angle is 18°.

Each exterior angle of a regular 25-gon = 360/25 = 14.4 deg. and each interior angle = 165.6 deg. Further, the sum of the interior angles = 4140 deg.

Answer: Each interior angle of a polygon of 23 sides = 164.35°.

Polygon Formula

The important polygon formulas are: The sum of interior angles of a polygon with “n” sides =180°(n-2) Number of diagonals of a “n-sided” polygon = [n(n-3)]/2. The measure of interior angles of a regular n-sided polygon = [(n-2)180°]/n. The measure of exterior angles of a regular n-sided polygon = 360°/n.

The sum of all interior angles of a regular polygon is calculated by the formula S=(n-2) × 180°, where 'n' is the number of sides of a polygon.

To calculate the number of sides of the polygon, divide 360 by the amount of the exterior angle. For example, if the exterior angle is 60 degrees, then dividing 360 by 60 equals 6, which is the number of sides the polygon has.

A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2) * 180 / n.

What is the sum of the exterior angles of a polygon with n sides? ›

If a regular polygon has n sides, then the sum of its exterior angles is 360∘. No matter what the size of the polygon is, the sum of the exterior angles will always add up to 360∘.

Thus, the given polygon has 18 sides.

The exterior angle of a regular polygon is formed by extending one side of the polygon outwards . The measure of an exterior angle is always equal to 360 divided by the number of sides in the polygon . Therefore , if an exterior angle measures 18 ° , the regular polygon must have 360/18 = 20 sides .

In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four-sided polygon. The sum of any icositetragon's interior angles is 3960 degrees.

Expert-Verified Answer

Hence, the measure of one interior angle of the given regular polygon with 23 sides is 164.3 degrees.

Find the sum of the interior angles of a 22-gon. Since the polygon has 22 sides, we can substitute this number for n: (n 2)180˚= (22 2)180˚= 20180˚= 3600˚.