Question bank: Polygon Angles

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Question 1:

Medium

Joana is drawing a mosaic with regular polygons and realizes that for the pieces to fit perfectly, the sum of the angles at each vertex must be equal to 360 degrees. Considering that Joana will use only equilateral triangles, squares, and regular hexagons in her mosaic, determine: a) The internal angle of an equilateral triangle, a square, and a regular hexagon. b) How many equilateral triangles, squares, and/or regular hexagons are needed for the sum of the angles at a vertex of the drawing to be exactly 360 degrees. c) Discuss whether it is possible to create a mosaic using only one type of polygon (equilateral triangle, square, or regular hexagon), where the angles at each vertex sum up to 360 degrees. If possible, indicate which of the polygons could be used for this purpose, and if not possible, explain the reason.

Polygon Angles

Question 2:

Medium

In a new project, Ana decided to decorate the floor of her living room with regular hexagonal tiles. Knowing that a hexagon is a polygon with 6 sides, answer the following questions: a) Without using formulas, calculate the sum of the measures of the internal angles of this regular hexagon. b) Determine the measure of just one internal angle of the hexagon. c) If we draw a line from the center of the hexagon to the middle of one of the sides, what will be the relationship between the internal angle and the external angle of the hexagon in this situation?

Polygon Angles

Question 3:

Medium

João was building a mosaic with regular polygons and came across a regular pentagon. He would like to know the internal and external angles of this regular pentagon, but he does not know how to calculate these measures without using formulas. a) Help João find the sum of the internal angles of the pentagon by dividing the pentagon into triangles and calculating the sum of the internal angles of each triangle. b) Then, find the measure of an internal angle of the pentagon by dividing the sum of the internal angles found in item a by the number of internal angles of the pentagon (5). c) Finally, calculate the measure of the external angle of the pentagon by subtracting the value found in item b from a right angle (90°).

Polygon Angles

Question 4:

Very Easy

A farmer is building a new pasture for his cows to graze. He wants to fence an area in the shape of a regular pentagon, which has five sides of equal length and five internal angles of the same measure. If the measure of one of the internal angles of the pentagon is 108 degrees, calculate the measure of each of the other internal angles of the pentagon.

Polygon Angles

Multidisciplinary Question

Question 5:

Easy

What is the measure of the sum of the interior angles of a regular hexagon?

Polygon Angles

IARA TIP

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