Is there a maximum number of obtuse exterior angles that any polygon can have if so what is the maximum if not why not?

Yes, there is a maximum number of obtuse exterior angles that any polygon can have. The maximum is three. A polygon can have no acute interior angles. It is always possible to fit four copies of a quadrilateral about a point because their angle measures will sum to 360°.

What is the maximum number of obtuse angles that a?

Answer: The sum of the angles of a quadrilateral is 360°. Hence only 3 obtuse angles are possible to maintain this sum.

Can a polygon have all obtuse angles?

For the interior angle to be a whole number, the exterior angle is also a whole number. The sum of the exterior angles of a simple (not self-intersecting) polygon is 360 degrees, for all possible numbers of sides. To keep all the interior angles obtuse, the polygon has to be convex.

How many maximum exterior angles can a regular polygon have?

120°
(b) The maximum exterior angle possible for a regular polygon is 120°.

How many obtuse angles can a polygon have?

A polygon can only have three obtuse exterior angles. Here is why. An angle is obtuse if its measure is between 90 and 180 degrees.

Which is the maximum number of obtuse angles that a quadrilateral can have?

A quadrilateral can have all four angles as obtuse.

What is the maximum number of obtuse angles that a quadrilateral can have class 8?

3 obtuse angles
As we know, an obtuse angle is an angle between 90 degrees to 180 degrees. The sum of the interior angles of a quadrilateral is equal to 360o. So all the angles can’t be obtuse since then the sum will more than 3600. Therefore a maximum of 3 obtuse angles that a quadrilateral have.

Which is the maximum number of obtuse angle that a quadrilateral can have?

Can a polygon have 3 obtuse angles?

The sum of three angles, each greater than 90 degrees, is greater than 270 degrees and hence it is not possible for all three to be obtuse.

How many obtuse exterior angles can a polygon have?

A polygon can only have three obtuse exterior angles. Here is why. An angle is obtuse if its measure is between 90 and 180 degrees. Let’s say than angle A is obtuse. Then, its measure is between 90 and 180 degrees, and its measure can be represented by 90 + n, where “n” is a positive number (between 0 and 90 degrees).

What is the maximum number of sides a convex polygon can have?

We will show that the maximum number of sides is 6. The sum of the interior angles of a convex polygon of n sides is ( n − 2) 180 ∘. Hence the sum of the exterior angles is n 180 ∘ − ( n − 2) 180 ∘ = 360 ∘. It follows that we can not have 4 or more obtuse exterior angles that is 4 or more acute interior angles.

How many acute angles can a convex polygon have?

Any convex polygon can have at most 3 acute interior angles. For any acute interior angle, the exterior angle will be greater than 90 degrees. The sum of all exterior angles in a polygon is always 360 degrees, so there cannot be 4 or more acute interior angles.

How many obtuse angles does a regular pentagon have?

So you must have 5 sides because a regular pentagon has 108 interior angles, and a 108 angle is an obtuse angle. Maybe your teacher wants you to do it this way: Since an obtuse angle is one greater than 90 You could get the answer by the inequality Multiply through by n.