Obtuse Angle: Definition, Facts, Examples

What is an Obtuse Angle?

Obtuse angle is a type of angle that always measures greater than 90° but less than 180°. This means it is wider than a right angle, which is exactly 90°, yet it does not open as far as a straight angle, which measures 180°. Obtuse angles occur in geometry when two rays meet at a point and spread apart to form a wide opening.  

For example, if ∠ABC = 120°, it is an obtuse angle because the measure lies between 90° and 180°. Similarly, ∠XYZ = 150° is also an obtuse angle for the same reason.  Both of these angles open wider than a right angle but do not stretch into a straight line.

Read More: Median of a Triangle 

Obtuse Angle Definition

Obtuse angle is defined as an angle that measures more than 90 degrees but less than 180 degrees. This means it is wider than a right angle, but not as wide as a straight angle. In geometric terms:

• An angle measuring 90° is known as a right angle.

• An angle measuring 180° is known as a straight angle.

So, any angle that is greater than 90° but less than 180° falls into the category of an obtuse angle. 

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How to Construct an Obtuse Angle?

Let us learn the steps to draw an obtuse angle using a protractor. In this example, we will construct an obtuse angle measuring 150°.

Step 1: Draw a straight line using a ruler and name one endpoint A. This will be the vertex of the angle.

Step 2: Place the centre hole of the protractor exactly on point A.

Step 3: Make sure the baseline of the protractor is aligned with the straight line.

Step 4: On the outer scale of the protractor, find 150° and mark a small dot at that point.

Step 5: Label this new point as B.

Step 6: Remove the protractor and use a ruler to join A and B with a straight line.

The angle ∠A formed is 150°, which lies between 90° and 180°. Hence, it is an obtuse angle.

Read More: Area of Triangle

Obtuse Angle Triangle

An obtuse angled triangle, also called an obtuse triangle, is a type of triangle in which one of the interior angles is greater than 90° but less than 180°. 

Since the sum of all three interior angles in a triangle is always 180°, if one angle is obtuse, the other two must be acute angles (each measuring less than 90°). This balance ensures the angle sum property of triangles is maintained.

Obtuse Angle Triangle Facts

The following are important facts that describe the nature of an obtuse triangle:

• An obtuse triangle has exactly one obtuse angle, which measures more than 90° and less than 180°.

• The other two angles are always acute (less than 90°), because the sum of all interior angles in a triangle is always 180°.

• A triangle cannot be both right-angled and obtuse-angled, since a right angle (90°) would leave only 90° for the other two angles, which must then be acute.

• The side opposite the obtuse angle is always the longest side of the triangle.

• An equilateral triangle (with all three angles equal to 60°) can never be obtuse.

• An obtuse triangle may be isosceles (two sides equal) or scalene (all sides different), but never equilateral.

• In coordinate geometry, the largest interior angle in any triangle can help classify it as obtuse.

Also read: Area of equilateral triangle

Acute and Obtuse Angles Difference

Understanding the difference between acute and obtuse angles is important when learning geometry. An acute angle measures less than 90°, while an obtuse angle measures more than 90° but less than 180°.

The following comparison shows the degree ranges and examples of each angle type:

• Acute Angle: 0° < angle < 90° (Examples: 30°, 60°, 85°)

• Obtuse Angle: 90° < angle < 180° (Examples: 120°, 150°, 175°)

In simple terms, acute angles are narrower, and obtuse angles are wider. A triangle can have either three acute angles (acute triangle) or one obtuse angle (obtuse triangle), but it cannot have both a right angle and an obtuse angle at the same time.

Obtuse Angles Real Life Examples 

Obtuse angles can be found all around us in daily life, not just in geometry class. Some common real-life examples include:

• The angle formed by the hands of a clock at 10:10 or 1:50 is obtuse, as it lies between 90° and 180°.

• The tilted blades of a ceiling fan

• The backrest of a reclining chair when leaned backward

• A pair of scissors when opened widely

• A laptop screen when it is partially open

In geometry, obtuse angles appear in many familiar shapes. In a rhombus or parallelogram, two of the four angles are usually obtuse.

Obtuse Angles Solved Examples

1:  An angle measures 118°. Is it an acute, right, or obtuse angle?

Solution: An obtuse angle is more than 90° and less than 180°.

Since 118° is greater than 90° and less than 180°, it is an obtuse angle.

2: In triangle ABC, two of the angles measure 35° and 28°. What is the measure of the third angle? Is the triangle obtuse?

Solution: The sum of all angles in a triangle is 180°.

Third angle = 180° – (35° + 28°) = 180° – 63° = 117°

Since 117° is more than 90°, it is an obtuse angle.

3: An angle measures 91°. What type of angle is it?

Solution: 91° is just slightly more than 90°, so it is greater than a right angle but still less than 180°.
That means it is an obtuse angle.

Also Read: Perimeter of a Triangle

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