Table of Content

• What is an obtuse angle?
• Obtuse Angle Degree
• Obtuse Angle Triangle
• Obtuse Angle Parallelogram
• Right Acute Obtuse Angle

Characteristics	Definition	Diagram
Right Angle	The angle that is equal to 90° is called right angle.
Acute Angle	The angle that is less than 90° is called acute angle.
Obtuse Angle	The angle that is greater than 90° is called acute angle.

Read More,

• Types of Angles
• Lines and Angles
• Pairs of Angles 

Solved Examples on Obtuse Angle

Example 1: In triangle PQR, if angle P measures 60° and angle Q measures 45°, determine the measure of angle R.

Solution:

For triangle PQR, the sum of its interior angles equals 180°. Using this:

Angle P + Angle Q + Angle R = 180°

Given that Angle P = 60° and Angle Q = 45°:

60° + 45° + Angle R = 180°

⇒ 105° + Angle R = 180°

⇒ Angle R = 180° – 105°

⇒ Angle R = 75°

Example 2: The exterior angle of a polygon is measured at 130°. Calculate the corresponding interior angle.

Solution:

For any polygon, the exterior angle plus its corresponding interior angle forms a straight line, which measures 180°. Therefore:

Exterior angle + Interior angle = 180°

Given the exterior angle = 130°:

130° + Interior angle = 180°

⇒ Interior angle = 180° – 130°

⇒ Interior angle = 50°

Example 3: If an angle measures 160°, find its complement.

Solution:

The complement of an angle is the difference between the angle and 90°.

Given angle = 160°:

Complement = 90° – 160°

⇒ Complement = -70°

However, as a complement can’t be negative, it implies that the given angle of 160° is an obtuse angle itself and doesn’t have a complement within the defined range of angles (0 to 90°).

Example 4: In a quadrilateral, one of the angles measures 125°. Is this angle obtuse?

Solution:

Yes, an angle measuring 125° is greater than 90°, so it is classified as an obtuse angle.

Example 5: An angle measures 150°. If it is a part of a triangle can this angle be an obtuse angle?

Solution:

Absolutely, since an obtuse angle falls between 90 and 180° an angle measuring 150° fits into the range and can be classified as obtuse.

Example 6: In a pentagon one angle measures 110° and another measures 95°. Are these angles obtuse?

Solution:

Among the two angles given the 110-degree angle is an obtuse angle as it is larger than 90° whereas the 95-degree angle is acute as it’s less than 90°.

Example 7: Within a hexagon, an angle measures 135°. Does this angle fit the description of an obtuse angle?

Solution:

Yes, an angle that measures 135° surpasses 90° yet remains less than 180°, aligning with the characteristics of an obtuse angle.

Example 8: If an angle measures 170°, would it qualify as an obtuse angle?

Solution:

Absolutely, an angle that measures 170° falls within the range of obtuse angles since it exceeds 90° but remains below 180°. Hence, it is categorized as an obtuse angle.

Obtuse Angle – Practice Questions

Q1: Identify an obtuse angle in your surroundings and measure its approximate degree.

Q2: Given an angle measuring 100°, determine if it is acute, obtuse, or neither.

Q3: Draw an obtuse angle using a protractor and measure its degree.

Q4: Calculate the measure of an obtuse angle that is supplementary to a 60-degree angle.

Q5: Identify and classify three obtuse angles within a shape or figure.

Obtuse Angle – FAQs

What is the Opposite of an Obtuse Angle?

The opposite of an obtuse angle is an acute angle, which measures less than 90°.

Can an Obtuse Angle be a Part of a Right-Angled Triangle?

No, by definition, an obtuse angle is larger than a right angle, which measures 90°. Therefore, it cannot be part of a right-angled triangle.

​Are there Real-Life Examples of Obtuse Angles?

Yes, examples include the angle formed by the minute and hour hands on a clock when it is between 3 and 6.

How does Understanding Obtuse Angles Benefit in Real-World Applications?

Understanding obtuse angles is crucial in fields like architecture and engineering, where precise angle measurements are essential for designing structures and systems.

Can an Obtuse Angle be Complementary to Another Angle?

No, because the sum of two complementary angles is always 90°, and an obtuse angle already exceeds this measure.

What is Obtuse Angle Triangle?

A triangle with an obtuse angle is called as obtuse angle triangle.

Can Two Obtuse Angle be Supplementary?

No, two obtuse angles cannot be supplementary as the sum of two obtuse angle is greater than 180°.

How Many degrees is an Obtuse Angle?

Degrees greater than 90 degree and less than 180° is an obtuse angle.

What is Acute and Obtuse Angle?

The angle less than 90° is called acute angle and the angle greater than 90°and less than 180° is called obtuse angle.