# What is the largest possible number of acute angles

• 22-16

#### 22-16

What is the largest possible number of acute angles that a 2001-gon (shape with 2001 sides) can have if no two sides cross each other [?]

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Depends on how you measure the angles.

If the angle at a concave vertex is measured externally to the polygon, then I can give you 2000 acute angles, and can probably give you the 2001-st as well.

Hurkyl

It is possible to make a 2001-gon with 1334 acute internal angles.

## 1. What is an acute angle?

An acute angle is an angle that measures less than 90 degrees.

## 2. What is the largest possible number of acute angles in a shape?

The largest possible number of acute angles in a shape is dependent on the number of sides the shape has. For example, a triangle can have a maximum of 3 acute angles, while a square can have a maximum of 4 acute angles.

## 3. Can a shape have an infinite number of acute angles?

No, a shape cannot have an infinite number of acute angles. As the number of sides of a shape increases, the size of each angle decreases, eventually becoming a straight line and no longer an acute angle.

## 4. What is the minimum number of acute angles a shape can have?

The minimum number of acute angles a shape can have is 0. A shape with 0 acute angles would be a straight line.

## 5. Are there any shapes that only have acute angles?

No, all shapes have a combination of acute, obtuse, and/or right angles. A shape with only acute angles would not have any sides longer than the others, which is not possible in a closed shape.