Table of Contents

Last modified on August 3rd, 2023

An obtuse angle is defined as an angle that measures more than 90° and less than 180°. In other words, any angle that lies between 90° and 180° is an obtuse angle.

A few more examples of obtuse angle are shown below:

- One angle in an obtuse angle triangle
- All angles of a regular polygon with five or more sides
- Blades of a ceiling fan
- A coat hanger
- Hands of a wall clock showing 8’ o clock
- An elevation or a staircase
- A house ceiling
- A fully opened cupboard door
- The angle at the bottom of the pot that holds a plant
- The angle at the bottom of some coffee mug
- A book wide open
- Most corners of our room

**Choose from the given options the obtuse angles.**

Solution:

As we know,

Obtuse angles are angles measuring more than 90° and less than 180°,

Hence, options (b), (c), and (d) are obtuse angles.

**Which of the following options given in the clock timing represents an obtuse angle?**

Solution:

As we know,

Obtuse angles are angles measuring more than 90° and less than 180°,

Hence, options (a), (b), (c), and (d) are obtuse angles.

**Find x in the given triangle and state whether it is an obtuse angle triangle**

Solution:

As we know,

The sum of the interior angles in a triangle = 180°,

Thus,

In △ABC,

∠ABC + ∠BCA + ∠CAB = 180°, here ∠ABC = 44°, ∠BCA = 32°

44° + 32° + ∠CAB = 180°

∠CAB = 180° – (44° + 32°)

∠CAB = (x°) = 104°

Since ∠CAB measure more than 90° and less than 180°, △ABC is an obtuse angle triangle

**Identify the obtuse angles in the given polygon ABCDEF.**

Solution:

As we know,

The sum of the interior angles of a hexagon = 720°

Thus,

∠ABC +∠BCD + ∠CDE + ∠DEF + ∠EFA +∠FAB = 720°

132° + 82° + ∠CDE + 88° + 107° + 142° = 720°

∠CDE = 720° – 551°

∠CDE = (x°) = 169°

Thus ∠ABC, ∠EFA, and ∠FAB are obtuse angles.

The main difference between an acute and an obtuse angle is that an acute angle always measures less than 90°, whereas an obtuse angle measure more than 90° and less than 180°.

**Ans**. There is only one obtuse angle in an obtuse triangle.

**Ans**. No, a triangle cannot have two obtuse angles because the sum of the three angles in a triangle is always 180°. If there are two obtuse angles that measure more than 90°, the third angle will have a negative value, which is impossible.

**Ans**. No, a quadrilateral cannot have four obtuse angles.

**Ans**. No, a right triangle cannot have any obtuse angles.

**Ans**. A trapezoid cannot have four obtuse interior angles.

**Ans**. The bisector of an obtuse angle forms two acute angles that have the same measure.

Last modified on August 3rd, 2023