What is the maximum number of obtuse angles a triangle can have? A. 2 B. 0 C. 1 D. 3

Question

UpStudy AI · Accepted Answer

To determine the maximum number of obtuse angles a triangle can have, we need to consider the properties of triangles and the definition of obtuse angles.

1. **Definition of an obtuse angle**: An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees.

2. **Sum of angles in a triangle**: The sum of the interior angles of any triangle is always 180 degrees.

Now, let's analyze the options:

- If a triangle had **3 obtuse angles**, the minimum sum of the angles would be $$3 	imes 91 = 273$$ degrees, which exceeds 180 degrees. Therefore, a triangle cannot have 3 obtuse angles.

- If a triangle had **2 obtuse angles**, the minimum sum of those two angles would be $$2 	imes 91 = 182$$ degrees. This also exceeds 180 degrees, so a triangle cannot have 2 obtuse angles.

- If a triangle had **1 obtuse angle**, the maximum it could be is 179 degrees. The remaining angle would then be $$180 - 179 = 1$$ degree, which is valid. Thus, a triangle can have 1 obtuse angle.

- A triangle cannot have **0 obtuse angles** if it has at least one angle, but it can have all angles acute (less than 90 degrees).

Based on this analysis, the maximum number of obtuse angles a triangle can have is:

**C. 1**
A triangle can have a maximum of 1 obtuse angle.

What is the maximum number of obtuse angles a triangle can have? A. 2 B. 0 C. 1 D. 3

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Geometry Questions