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How many acute angles can a convex polygon have?

seo-qna
Last updated date: 13th Jun 2024
Total views: 371.4k
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Answer
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Hint: Here, we will use the concept of the lines and angles of geometry. The sides and angles are generally known as part of any shape. So by calculating the maximum number of exterior angles a polygon can have we will get the number of acute angles a convex polygon can have.

Complete step by step solution:
It is given that the figure is a convex polygon which is a closed plane figure which is defined as the two dimensional figure which is lying on a single plane. Line segments are used to form a figure which is also known as the edges of the figure. The points at which these edges meet are known as the vertices of the figure.
Figures are generally known as polygons and these polygons generally vary according to the number of the edges of the figure.
So if a polygon has an interior acute angle which means that its corresponding exterior angle is greater than \[90^\circ \].
So, if a polygon has four sides or more than four sides which mean that the sum of the exterior angle will be greater than \[360^\circ \] which is not possible because the sum of all the exterior angle of a polygon must be equal to \[360^\circ \].
Therefore, a polygon can have a maximum of three acute angles in it.

Hence, maximum of three acute angles a convex polygon can have.

Note:
Geometry is the branch of mathematics that deals with points, lines and shapes. A triangle is a polygon with three edges/sides and three vertices. Side is one of the straight line segments which is used to construct/draw a polygon. When two or more lines cross each other in a plane, they are called intersecting lines and the point where these lines intersect is called a Point of Intersection.