Web24 sep. 2024 · How many sides does a regular polygon have if the sum of its interior angles is? The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. Web22 jul. 2024 · Number of sides of the polygon is 12. As it is a regular polygon, all exterior angles are equal and are 30°. Hence number of sides of the polygon is 360°/30°=12. What polygon has exterior angle of 30? dodecagon Since all the angles are congruent, 30a=360 , and a=12 . Since a=s , s=12 , so the polygon has 12 sides.
How many sides does a regular polygon have if each of its …
Some regular polygons are easy to construct with compass and straightedge; other regular polygons are not constructible at all. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, and they knew how to construct a regular polygon with double the number of sides of a given regular polygon. This led to the question being posed: is it possible to construct all regular n-gons with compass and straightedge? If not, which n-gons ar… Web15 jun. 2024 · Just divide the sum of the angles by the number of sides. Regular Polygon Interior Angle Formula: For any equiangular n−gon, the measure of each angle is (n − 2) × 180 ∘ n. Figure 5.27.3. In the picture below, if all eight angles are congruent then each angle is (8 − 2) × 180 ∘ 8 = 6 × 180 ∘ 8 = 1080 ∘ 8 = 135 ∘. Figure 5.27.4. solar powered scarecrow
Interior Angles of Regular Polygons - A Plus Topper
Web7 sep. 2016 · Diagonals of a Regular Octagon. An octagon is any eight-sided polygon, and the sum of its angles is 1080°, as we saw above. In a regular octagon, each angle = 1080°/8 = 135°. That angle is the supplement of a 45° angle. The regular octagon is the typical stop sign shape in many parts of the world. Web21 jan. 2024 · Regular polygons have equal side lengths and identical interior angle measures. In a regular polygon, all interior angles measure less than 180 degrees. In contrast, irregular polygons have ... Web11 jan. 2024 · Sometime during the mid 1600s, a mathematician felt the need for a descriptive word for a 12-sided polygon. The word dodecagon comes from the Greek, dōdeka-, which means 12, and + -gōnon, which means angled. Dodecagons can be regular, meaning all interior angles and sides are equal in measure. They can also be irregular, … solar powered rrfb