Question Video: Identifying an Obtuse Angle from Its Measure | Nagwa Question Video: Identifying an Obtuse Angle from Its Measure | Nagwa

Question Video: Identifying an Obtuse Angle from Its Measure Mathematics • First Year of Preparatory School

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Which of the following is an obtuse angle? [A] Option A [B] Option B [C] Option C [D] Option D [E] Option E

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Video Transcript

Which of the following is an obtuse angle? Options (A), (B), (C), (D), and (E).

In this question, we are asked to identify which of five given angles is obtuse. And we can do this by first recalling what is meant by an obtuse angle. An obtuse angle is one whose measure is between 90 degrees and 180 degrees. That is, the rotation required to rotate one side of the angle onto the other side is between a quarter turn and a half turn.

Of the given options, we can see that only option (D) has a measure between 90 degrees and 180 degrees. So it is the only obtuse angle.

We could stop here; however, we can also classify the angles in each of the other options.

First, if an angle has measure greater than 180 degrees, then it is a reflex angle. So the angle in option (A) with measure 220 degrees is a reflex angle.

Next, if an angle has measure between zero degrees and 90 degrees, then it is acute. So the angle in option (B) with measure 25 degrees is acute.

We can also recall that we call angles with measure 90 degrees right angles. So the angle in option (C) is a right angle.

Finally, we say that an angle with measure 180 degrees is a straight angle. So option (E) is a straight angle.

Hence, only option (D) shows an obtuse angle.

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