Understanding Obtuse Angles: Definition, Identification, and Properties

obtuse angle

An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees

An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees. In other words, it is an angle that is wider or “more open” than a right angle (90 degrees), but not wide enough to be a straight angle (180 degrees).

To identify an obtuse angle, you can use a protractor to measure the angle or use geometric properties if you know the measurements of other angles in the figure. Here’s how:

1. Using a protractor:
– Place the protractor on one arm of the angle, aligning the base of the protractor with the vertex (common endpoint) of the angle.
– Identify the scale on the protractor that starts at 0 degrees (usually placed at the right side).
– Read the measurement on the scale where the second arm of the angle intersects it.
– If the measurement is greater than 90 degrees but less than 180 degrees, the angle is obtuse.

2. By using geometric properties:
– If you know the measurements of other angles in a figure and the sum of the angles is greater than 180 degrees, you can infer the existence of an obtuse angle. Remember that the sum of angles in a triangle is always 180 degrees, and the sum of angles in a quadrilateral is always 360 degrees.

For example, if you have a triangle with two angles that measure 45 degrees each, the sum of these angles is 90 degrees. Since the sum of angles in a triangle is always 180 degrees, the third angle must be greater than 90 degrees to satisfy the relationship. Therefore, the third angle would be an obtuse angle.

It is important to note that an obtuse angle is one type of angle classified by its measure; there are also acute angles (less than 90 degrees) and right angles (exactly 90 degrees).

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