Obtuse Angle

What is an Obtuse Angle

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:

Obtuse Angles in Real Life

• 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.

Acute vs Obtuse Angle

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°.

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