Obtuse angle

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The obtuse angle is that arc that is formed from the union of two lines that measures more than 90º or π / 2 radians and less than 180º or π radians.

An obtuse angle, in other words, is one that measures more than a right angle, but less than a straight angle.

To explain it another way, let's imagine that we have a circumference (or a complete or perigonal angle of 360º). So, an obtuse angle will be greater than a quarter of the figure, but less than half of it.

An obtuse angle fulfills by having as a supplementary angle (with which it adds 180º) an acute angle. For example, an angle of 130º is supplemented by an angle of 50º.

However, being greater than 90º, an obtuse angle cannot be complementary to any other angle.

Another point to take into account is that the lines that form the obtuse angle are not perpendicular.

To learn more, we recommend you visit our article on types of angles.

The obtuse angle concept serves as a reference for analyzing geometric figures. For example, in the case of a triangle, it cannot have more than two obtuse angles because its internal angles must always add up to 180º.

For example, if one of the interior angles of a triangle is 100º, the other two must add up to 80º and are therefore necessarily acute angles.

Examples of obtuse angle

Some examples of obtuse angles are:

  • Obtuse triangle: One of its angles is obtuse, while the other two are acute (as explained above).

In the example above, γ would be an obtuse angle, facing the side with the longest length.

  • Rhombus: Two interior angles of the rhombus are acute, while the other two are obtuse, as we notice in the image below:

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