What is the maximum number of obtuse angles in a triangle? (2024)

FAQs

What is the maximum number of obtuse angles in a triangle? ›

In a triangle, only one obtuse angle

An obtuse triangle has one obtuse angle. The other two angles are acute angles.

An triangle cannot have two obtuse angles because the sum of all the angles of it cannot be more than 1800.

Answer and Explanation:

The shape which has the greatest number of obtuse angles is the myriagon. A myriagon has 10,000 sides and 10,000 angles! Each interior angle of a myriagon measures 179.964 degrees.

Only One 1. The reason for this is that in a triangle, the sum of all the angles must be equal to 180° and and obtuse angle is the one with its measure being more than 90°. So, the other two angles cannot be obtuse as in that case, the sum will exceed 180°. Therefore, only one obtuse angle.

An obtuse angle is defined as an angle that is greater than 90° and less than 180°. We know that the sum of all the four interior angles of a quadrilateral is 360 degrees. All angles cannot be obtuse. Therefore, the maximum number of obtuse angles can be 3.

Meaning of Min (Minimum)

In a given set of data, the smallest or the least number is said to be the minimum number. It can be easily detected by arranging the given data in descending or ascending order. For example, the given series of numbers is 167, 897, 69, 301, 999, 294.

A triangle whose any one of the angles is an obtuse angle or more than 90°, then it is called an obtuse-angled triangle or obtuse triangle. The sum of the interior angles of the obtuse triangle is equal to 180° only. This means the angle sum property for any triangle remains the same.

Obtuse angles are greater than 90° , so the sum of 2 obtuse angles is greater than 180°. If you include the third angle, the sum of all three angles would be even larger. It is not possible for a triangle to have 2 obtuse angles.

The greatest number of acute angles that a triangle can contain is three. An acute angle is defined as an angle that has a measure of less than 90 degrees. The total of the degrees of the angles in any triangle always adds up to 180 degrees.

What shape has all obtuse angles? ›

This octagon has all obtuse interior angles. Some shapes have some obtuse angles, but also other types of angles. Both the parallelogram and the trapezoid have two obtuse angles, but also other angles. Obtuse angles are also formed when two straight lines cross and they are not perpendicular.

In other words, it lies between 90° and 180°.

Hence, a triangle can have only one obtuse angle. Q.

In Mathematics, “an obtuse angle is an angle which is greater than 90° and less than 180°”.

Angles between 0 and 90 degrees (0°< θ <90°) are called acute angles. Angles between 90 and 180 degrees (90°< θ <180°) are known as obtuse angles.

The sum of the interior angles of the obtuse triangle is equal to 180° only. This means the angle sum property for any triangle remains the same.

Angles between 90 and 180 degrees (90°< θ <180°) are known as obtuse angles. Angles that are 90 degrees (θ = 90°) are right angles. Angles that are 180 degrees (θ = 180°) are known as straight angles. Angles between 180 and 360 degrees (180°< θ < 360°) are called reflex angles.

Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees.

A triangle can have all the three angles greater than 60∘.