Obtuse Angle

To recall we know that the two rays intersecting or meeting at a point form an angle. If that angle is more than 90 degrees and less than 180 degrees, it is known as an Obtuse angle. The point is said to be vertex and the rays are said to be the sides of an angle. The measurement between the two rays is measured in degrees. An angle is denoted by a single alphabet or three alphabets.


Example: From the figure, ∠XYZ is an Obtuse angle. XY and YZ are the sides of the angle and Y is the point of intersection called the vertex. Angles are commonly measured in terms of degree. Here, it is 120 degrees.

(image will be uploaded soon)


Angles are classified according to their sizes as follows

  • Acute angle( angle less than 900)

  • Obtuse angle( angle greater than 900 less than 1800)

  • Right angle ( angle measures 900)

  • Straight angle( angle measures 1800)

  • Reflex angle( angle greater than 1800)

In this article let us study what is an obtuse angle, obtuse angle definition, obtuse angle degree, and obtuse angle examples.


What is an Obtuse Angle?

Obtuse Angle Definition:

We can define the obtuse angle is an angle whose measure is above 900 and below 1800 is said to be an obtuse angle. Also, we can define the obtuse angle as the angle between 900 and 1800 i.e angle between a right angle and straight angle. Obtuse angle degree is greater than 900 and less than 1800.


(image will be uploaded soon)


Obtuse angle Real - Life Example:

Imagine tilting a car seat back so that you can be seated comfortably. You'd push it in the back of the position, closer to lying flat. Where the seat's bottom and the back meet would be an obtuse angle because you've pushed them back beyond a 90-degree angle. It might look something like this:


The dotted line represents the original position of the seat. And the angle so formed after pushing the seat backward is an obtuse angle.

(image will be uploaded soon)


Imagine some more obtuse angle real-life examples.


How to Draw Obtuse Angle?

Now let us see how to draw obtuse angle


Following are the steps for how to draw obtuse angle using a protractor:

  1. Draw a straight line with a ruler.

  2. Mark the endpoints of the sediment as A and B

  3. Then take a protector and keep its center line on the starting point of the line segment.

  4. Start measuring the 0 degrees from the right side.

  5. Mark any degree between 900 to 1800. Label it as C

  6. Join the points A and C. Suppose here in this figure we are marking 1290.

  7. We angle CAB as the obtuse angle whose measure is 1299.

(image will be uploaded soon)


The Obtuse Angle Polygons

Now let us study how obtuse angle is formed by some of the examples of a polygon


Obtuse Angle of a Triangle

(image will be uploaded soon)


Some of the properties related to the obtuse-angled triangle are:

  • The obtuse angle of a triangle is where one of its angles of a triangle is greater than 900 and less than 1800

  • An equilateral triangle cannot have an obtuse angle because all its angles are equal and all three angles cannot be greater than 900

  • In an obtuse angles triangle, the side opposite to the obtuse angle is the longest side of the triangle. 

  • Similarly, a triangle cannot have a right angle and obtuse angle at the same time because if one of the angles of a triangle is obtuse, the other two angles of a triangle must be acute.


Obtuse Angle of a Rhombus

(image will be uploaded soon)


In a rhombus, opposite angles are congruent to each other. And also A rhombus has two opposite acute angles and two opposite obtuse angles. The sum of two consecutive internal angles is supplementary i.e 1800. It means that if an acute angle and obtuse angle is added, its sum is 1800.


Obtuse Angle of a Parallelogram

(image will be uploaded soon)


In a parallelogram, the opposite sides are parallel to each other. And in parallelogram  two angles are acute angles and two angles are obtuse angles. Here in parallelogram ABCD, ∠DAB and ∠DCB are the acute angles, whereas ∠ABC and ∠ADC are the obtuse angles.in parallelogram too, if an acute angle and obtuse angle is added, its sum is 1800.


Let us solve some obtuse angle examples.


Solved Examples

Obtuse Angle Example


Example 1: Identify the Obtuse angles from the figure.

(images will be uploaded soon)


Solution: Figure 2 is an obtuse angle because obtuse angle degree is greater than 900  and less than 1800


Example 2: If the reflex angle of the given rays is 250°, then what will be the measure of the other interior angle?


Solution:


Given that, the measure of the reflex angle = 250°


To find the unknown interior angle, we know that,


Reflex angle + Unknown angle = 360°


Let the unknown angle be “x”.


Let us substitute the value of the reflex angle 


250° + x = 360°


x = 360° – 250°


x = 110°


Hence, the unknown angle obtained is an obtuse angle which measures 110°.

FAQ (Frequently Asked Questions)

1. What is a Straight Angle?

Straight Angle Definition 

When one arm is moved from the vertex such that both the arms are opposite to each other and forms a straight line then it is called a straight angle. The measure of a straight angle degree is 1800. Below is the straight angle diagram


(image will be uploaded soon)


From the above figure, OY and OX are the sides of the angle. And O is the vertex of the angle. The sides of the angle form 180o with the line called a straight angle.

2. What is Zero Angle?

As the name implies, an angle that measures 00 is called a zero angle. You can assume two sides of an angle overlaps each other.

3. What is an Acute Angle?

Acute Angle Definition:

We can define the Acute angle is an angle whose measure is above 00 and below 900 is said to be an acute angle. Also, we can define the acute angle as the angle between 00 and 900 i.e angle between zero angle and right angle. The acute angle degree is greater than 00 and less than 900.

(image will be uploaded soon)