**Acute Angled triangle** – When all the Angles of a Triangle are Acute angles ( less than 90°), we call such a triangle as an Acute angled triangle.

For Example – **∆ ABC is an Acute Angled Triangle as all the three angles i.e, ∠BAC, ∠ACB and ∠ABC are less than 90°( acute angle).**

**Right Angled Triangle** – When one angle of a triangle is 90° and the other two angles are acute ( less than 90°) then we call such a triangle as a Right angled triangle.

For Example – **∆ ABC is a Right Angled Triangle as ∠BAC is 90° ( right angle ) and ∠ACB and ∠ABC are less than 90° ( acute angle ).**

**Obtuse angled triangle** – If one angle of a triangle is obtuse ( greater than 90°) and other two are acute ( less than 90°), we call such a triangle as Obtuse angled triangle.

For Example – **∆ABC is an Obtuse Angled triangle as ∠BAC is 110° (obtuse angle) and ∠ACB and ∠ABC are acute angle (less than 90°). **

## Acute Angled Triangle, Right Angled Triangle and Obtuse Angled Triangle – Examples

**EXAMPLE 1**

If the measure of the angle of the triangle are 56 ˚ , 49 ˚ and 75 ˚, then the triangle is?

**EXPLANATION**

**Acute Angled Triangle** – When all the Angles of a Triangle are Acute angles ( less than 90°), we call such a triangle as an Acute angled triangle.

**Right Angled Triangle** – When one angle of a triangle is 90° and the other two angles are acute ( less than 90°) then we call such a triangle as a Right angled triangle.

**Obtuse angled Triangle** – If one angle of a triangle is obtuse ( greater than 90°) and other two are acute ( less than 90°), we call such a triangle as Obtuse angled triangle.

here,

56 ˚ < 90 ˚

49 ˚ < 90 ˚

75 ˚ < 90 ˚

Since, all the three angles of triangle are **acute angles** (**less than 90˚**)

Hence, the triangle is An **Acute Angled Triangle. **

**EXAMPLE 2**

If the measure of the angle of the triangle are 90 ˚ , 54 ˚ and 36 ˚, then the triangle is?

**EXPLANATION**

**Acute Angled Triangle** – When all the Angles of a Triangle are Acute angles ( less than 90°), we call such a triangle as an Acute angled triangle.

**Right Angled Triangle**– When one angle of a triangle is 90° and the other two angles are acute ( less than 90°) then we call such a triangle as a Right angled triangle.

**Obtuse angled Triangle** – If one angle of a triangle is obtuse ( greater than 90°) and other two are acute ( less than 90°), we call such a triangle as Obtuse angled triangle.

here,

**90 ˚ = 90 ˚
**54 ˚ < 90 ˚

36 ˚ < 90 ˚

Since, one angle is** 90˚** and the other two angles are acute angle (less than 90˚)

Hence, the triangle is a **Right Angled Triangle**

**EXAMPLE 3**

If the measure of the angle of the triangle are 93 ˚ , 55 ˚ and 32 ˚, then the triangle is?

**EXPLANATION**

**Acute Angled Triangle** – When all the Angles of a Triangle are Acute angles ( less than 90°), we call such a triangle as an Acute angled triangle.

**Right Angled Triangle** – When one angle of a triangle is 90° and the other two angles are acute ( less than 90°) then we call such a triangle as a Right angled triangle.

**Obtuse angled Triangle** – If one angle of a triangle is obtuse ( greater than 90°) and other two are acute ( less than 90°), we call such a triangle as Obtuse angled triangle.

here,

**93 ˚ > 90 ˚
**55 ˚ < 90 ˚

32 ˚ < 90 ˚

Since, one angle of a triangle is** obtuse **( **greater than 90˚** ) and other two are acute angles (less than 90˚)

Hence, the triangle is an **Obtuse Angled Triangle **

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