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Obtuse Angle and Its Examples

Referencing Styles : Harvard | Pages : 1

Types of Angles

There are six different types of angles that can be formed in geometry. These different angles have different names and they are – acute angle, right angle, obtuse angle, straight angle, reflex angle and a full rotation. The acute angles are any of the angles that are formed measuring less than 90 degree. Right angles are angles that can formed vertically straight so that a box can be formed with the 0 degree line. Obtuse angles are those angles that are formed beyond the 90 degree angle and above the 180 degree line. Straight angles are measured at 180 degree and this angle points the totally opposite direction than 0 degree. Reflex angle is formed when the angle crosses the 180 degree angle but does not make a full rotation. A full rotation is the angle that completes a full circular rotation and is measured at 360 degrees.

Obtuse Angle and how it differs from a Reflex Angle    

Obtuse angles are any of the angles that are measured to be more than 90 degree and less than 180 degree. These angles should not be confused with reflex angles. This is worth mentioning specifically as reflex angles may look similar to obtuse angles. The actual difference between an obtuse angle and a reflex angle is that obtuse angles can range from anywhere between 90 degree and 180 degree. The reflex angles on the other hand can vary between 180 degree and all the way up to 360 degree. Obtuse angles are always bigger than all acute angles and are always lesser than all reflex angles when comes to measurement. The commonality that obtuse angles have with acute angles is that 89 different obtuse angles can be formed starting from 91 degree to 179 degree just like acute angles 1 degree to 89 degree. Reflex angles however, are different as 179 different reflex angles can be formed starting from 181 degree to 379 degree.

Example of an Obtuse Angle

Figure 1: Example of an Obtuse Angle

Example of an Reflex Angle 

Figure 2: Example of a Reflex Angle

From the above examples the obtuse angle can be clearly distinguished from the Reflex Angle. Here the ‘*’ symbol at the end of every number represents the degree of angle. Angles start at 0*. On the vertically opposite quadrant this angle becomes 360*. If the angle forms an extension of the 0 degree line horizontally, the angle thus formed as a result is 180 degree or a straight angle thus pointing the complete opposite direction compared to 0 degree. Any angle formed that bisects this line is 90 degree. The circle formed by the angles denote a full rotation and is measured at 360 degree. All angles that are formed beyond 90 degree and before 180 degree are known as obtuse angles. For example from Figure 1, the angle measuring 130 degree lies between 90 degree and 180 degree and hence this angle is an obtuse angle. Again from Figure 2, the angle measuring 205 degree lies between 180 degree and 360 degree and hence this angle is a reflex angle.

Real world Example

Real world examples of obtuse angles can be when a clock shows the time 1:45. It is because at this time the hour hand of the clock points away from 12 which forms a right angle with the minute hand that is pointing at 9. Therefore, the angle formed as a result is greater than 90 degree and less than 180 degree which could only be formed if the hour hand had been pointing 3. Similarly if the clock shows the time 4:00, the minute hand points to 12 and now to form a corresponding right angle, the clock needs to strike 3. Since the time 4 o’clock requires the hour hand to create a greater angle to be able to strike 4 the angle created as a result is an obtuse angle. If the time at the clock is 6 o’clock a straight angle is formed. Hence every hour after 6 o’clock and before 12 o’clock, reflex angles are formed by the clock. Also after every hour the hour hand of the clock completes a full rotation forming 360 degree. When the time in the clock is 7:15, the angle thus formed is still an obtuse angle and not a reflex angle as the angle here is measured clockwise.

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