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.
