Polygon + angle - practice problems
Number of problems found: 133
- Regular polygons
The number of sides of two regular polygons differ by 1. The sum of the interior angles of the polygons is in the ratio of 3:2. Calculate the number of sides of each polygon. - One side 4
One side of a regular octagon is 12 inches. Find the apothem and its area. - The apothem
The apothem of a regular hexagon is 5√3 inches. Find one of its sides and area. - The interior
The interior angle of a regular polygon is x. If x is 9° less than the average of 153° and 145°, find the number of sides of the polygon.
- n-gon
Gabo draws n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon? - Each with each
Five pupils from 3A class played table tennis. How many matches did they play with each other? - Interior angles - sum
For the sum s of the interior angles of a polygon, where n is the number of its sides, the relation s=(n−2)⋅180 degrees applies. How many sides does a polygon have if the sum of its interior angles is 900°? - Regular n-gon
In a regular n-angle polygon, the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon. - Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2).180 degrees.
- Angles of a hexagon
Find the interior angles of a hexagon if the sizes of the angles form an arithmetic sequence, and the smallest angle is 70°. - Polygon 42
Which polygon has 42 more diagonals than sides? - 9-gon
The sum of interior angles of 9-gon is: - Diagonals
What x-gon has 54 diagonals? - N-gon
How many diagonals have convex 30-gon?
- Candy - MO
Gretel deploys different numbers to the vertex of a regular octagon, from one to eight candy. Peter can then choose which three piles of candy to give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles t - Inner angles
The inner angles of the triangle are 30°, 45°, and 105° and its longest side is 10 cm. Calculate the shortest side length, and write the result in cm up to two decimal places. - Similarity n-gon
9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S1=190 dm², and the diagonal length GD is 32 dm. Calculate the area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm. - Center of gravity
In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity is T, find the area of the triangle ABT. - Complementary 81152
In a certain polygon, the ratio of the sum of the sizes of its internal angles and the sum of the sizes of the complementary angles is 2:5. How many vertices does this polygon have?
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