Acute, Right, and Obtuse Triangles

Types of Triangles:- ★ Triangles can be classified into three types on the basis of their Angles.

1. Acute angled triangle- In this type of Triangles all the angles in the triangle measure less than 90° Eg. 45°, 60°, 75°

2. Right angled triangle - In this type of triangle one of the three angles in the triangle measures 90° Eg.90°, 45°, 45°

3. Obtuse angled triangle - In this type of triangle one of the three Angles of a triangle measures more than 90° Eg.120°, 30°, 30°

Commonly asked questions : a) Can a triangle have more than 1 right angle ? Ans- No a triangle cannot have more than one right angle as if there are 2 right angles the their sum will be 180° and the third angle will exceed the sum. Therefore the construction is not possible.

b) Can a triangle have more than 1 obtuse angle ? Ans- No a triangle cannot have more than one obtuse angle. As we all know an obtuse angle is an angle measuring between 90° and 180°. Therefore as we have previously discussed that the sum of Angles will exceed 180° and the construction won't be possible

So there are three types of angles, $acute$, $right$, and $obtuse$. Here are their definitions:

An $acute$ angle is an angle whose measure is less than $90^\circ$. That is, in a pair of intersecting non-perpendicular lines, the smaller of the angles are $acute$.

A $right$ angle is an angle whose measure is equal to $90^\circ$. That is the measure of the angles of perpendicular lines.

An $obtuse$ angle is an angle whose measure is greater than $90^\circ$. That is, in a pair of intersecting non-perpendicular lines, the larger of the angles are $obtuse$.

Hope you understand!