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Obtuse Angles: An obtuse angle is an angle that measures more than 90° but is less than 180°. A simple example of an obtuse angle in everyday life is the angle formed between the minute hand and the hour hand on a clock at specific times. In this article, we’ll study the definition of an obtuse angle, its examples, and its properties.
What is an Obtuse Angle?
An obtuse angle is an angle that measures more than 90° but it is lesser than 180°. In simpler words, an obtuse angle lies between a right angle (90°) and a straight angle (180°).
Obtuse Angle Degree
As mentioned earlier, an obtuse angle is any angle that falls within the range of 90° to 180°. Some examples of obtuse angle measurements include 165°, 135°, 110°, 179°, and 91°. All of these angles are greater than 90° but do not exceed 180°.
How to measure an Obtuse Angle?
An Obtuse Angle can be measured using the Protractor. Follow the mentioned steps to find the angle.
- Place the centre of the Protractor at a fixed point O. This is where both the lines making the angle meet.
- Coincide the reference line on the Protractor with an arm of the angle at point O. This is the initial line (zero degrees).
- Another arm of the angle will now indicate the degree of angle formed.
- You will have to measure it from the initial hand in the anti-clockwise direction.
- If the angle we have is greater than 90 degrees and less than 180 degrees is an Obtuse angle.
Obtuse Angles in Real Life
Obtuse angles are commonly found in everyday life. Any angle that measures between 90° and 180° is considered an obtuse angle. For example, you might observe obtuse angles in the open wings of a book, the angle between two walls that aren’t perpendicular, or the way certain tools like scissors open.
Here are a few more examples of obtuse angles in real life:
- The angle formed between the hour and minute hands of a clock at 4 o’clock.
- The angle between the base of an open laptop and its screen.
- The angles that are created by the blades of a ceiling fan when they are tilted.
Obtuse Angle Triangle
An obtuse angle triangle is a type of triangle where one of the interior angles measures more than 90°. This characteristic distinguishes it from other types of triangles. Here are some key properties of an obtuse angle triangle:
Properties of Obtuse Angle Triangle
An obtuse triangle can be either isosceles (where two sides are of equal length) or scalene (where all sides are of different lengths). However, an equilateral triangle cannot be obtuse, as all its angles measure 60° each.
Longest Side: In an obtuse triangle, the side opposite the obtuse angle is the longest side.
According to the angle sum property of a triangle, a triangle cannot be both a right-angled triangle and an obtuse angle triangle simultaneously. This means that if a triangle has one obtuse angle, the other two angles must be acute (less than 90°).
In an obtuse triangle, the sum of the squares of the two shorter sides is less than the square of the longest side.
Acute and Obtuse Angles
Angles can be categorized based on their measurements:
- Acute Angles: Angles that measure less than 90°.
- Obtuse Angles: Angles that measure more than 90° but less than 180°.
Difference Between Acute Angles and Obtuse Angle
Acute Angle: The angle whose measure is less than 90° is said to be an acute angle.
Obtuse Angle: The angle that measures more than a right angle or 90° angle is said to be an Obtuse Angle.
Below given is the difference between Acute Angles and Obtuse Angles.
| Feature | Details |
|---|---|
| Acute Angle | Measure of the Acute Angle is always less than 90°. |
| Obtuse Angle | The Measurement of the Obtuse Angle is between 90° and 180°. |
| Acute Angle | A triangle can have more than one acute angle. |
| Obtuse Angle | A triangle cannot have more than one Obtuse Angle. |
| Acute Angle | An acute angle always measures less than a right angle. |
| Obtuse Angle | An Obtuse Angle is greater than a right angle but less than a straight angle. |
Important Points about the Obtuse Angles
Any angle that measures more than 90° and less than 180° is classified as an obtuse angle.
Obtuse Angle Triangle: In an obtuse angle triangle, the sum of the squares of the two shorter sides is less than the square of the longest side. This can be expressed mathematically as a2 + b2 < c2 , where c is the longest side of the triangle.
Obtuse Angles Examples
Q1. If a given angle (x) is obtuse then verify if x is obtuse if it measures as:
20°
60°
110°
105°
176°
Ans. If the given angle x is obtuse, then:
20° < 90°, therefore, x is not an obtuse angle if x = 20°.
60° < 90°, therefore, x is not an obtuse angle if x = 60°.
110° > 90°, therefore, x is an obtuse angle if x = 110°.
105° > 90°, therefore, x is an obtuse angle if x = 105°.
176° > 90°, therefore, x is an obtuse angle if x = 176°
Q2. Which angle is an Obtuse Angle?
Ans. Option C i.e. ∠125 is an obtuse angle.
Obtuse Angle Practice Questions
- Check if the following angles are obtuse: 85°, 145°, 92°, 180°. Draw these angles using a protractor.
- A triangle has angles measuring 40°, 120°, and 20°. What type of triangle is it? Explain your reasoning.
- In a triangle, two of the angles measure 35° and 105°. What is the measure of the third angle? Is this triangle an obtuse triangle?
- Identify an object in your surroundings that forms an obtuse angle. Describe the object and explain how the angle qualifies as obtuse.
- A triangle has sides measuring 7 cm, 24 cm, and 25 cm. Determine if this triangle is an obtuse triangle by applying the Pythagorean inequality.
Obtuse Angles FAQs
What is an obtuse angle?
An obtuse angle is any angle that measures more than 90° but less than 180°.
Can a triangle have more than one obtuse angle?
No, a triangle cannot have more than one obtuse angle because the sum of all angles in a triangle is 180°, and having more than one obtuse angle would exceed this total.
What is an example of an obtuse angle in real life?
A common example of an obtuse angle in real life is the angle formed between the hour and minute hands of a clock at 4 o'clock.
What are the 7 types of angles?
The seven types of angles are: Acute Angle: An angle that measures less than 90°. Right Angle: An angle that measures exactly 90°. Obtuse Angle: An angle that measures more than 90° but less than 180°. Straight Angle: An angle that measures exactly 180°. Reflex Angle: An angle that measures more than 180° but less than 360°. Full Angle: An angle that measures exactly 360°, forming a complete circle. Zero Angle: An angle that measures exactly 0°, where the two arms of the angle coincide.
