Some angles have special names.

  • A right angle has a measure of 90^\circ. It corresponds to one-quarter of a full turn.

  • A straight angle, which is just a straight line, has a measure of 180^\circ. It corresponds to one-half of a full turn.

  • A null angle has a measure of 0^\circ. You can imagine "closing" the angle until the two sides of the angle overlap. In this case, we don't have any turn, so its measure is zero!

  • A full angle has a measure of 360^\circ. You can imagine "opening" the angle until one of the sides goes all the way around. So, this is the angle between a ray and itself after it has made one full turn.

On a diagram, null and full angles can look the same, so it is up to us what we choose to call it.

FLAG

Which of the following shows a right angle?

EXPLANATION

An angle of 90^\circ has the same measure as one-quarter of a full turn.

Among the given options, the only 90^\circ angle is the following:

Therefore, the correct answer is II.

FLAG

Which of the following shows an angle of $90^\circ?$

a
b
c
d
e

Which of the following shows a right angle?

a
b
c
d
e

Which of the following is the closest to a right angle?

a
b
c
d
e

Which of the following shows a straight angle?

EXPLANATION

A straight angle has a degree measure of 180^\circ. This corresponds to one-half of a full turn.

Among the given options, the only straight angle is the following:

Therefore, the correct answer is III.

FLAG

Which of the following shows an angle of $180^\circ?$

a
b
c
d
e

Which of the following shows a straight angle?

a
b
c
d
e

Which of the following is the closest to a straight angle?

a
b
c
d
e

What type of angle is \angle RST, shown in the figure above?

EXPLANATION

Notice that the vertex of \angle RST is point S, not point T. So \angle RST is not a straight angle.

As a result, the two rays \overset{\longrightarrow}{SR} and \overset{\longrightarrow}{ST} of our angle coincide. So, we can think of \angle RST as:

  • A null angle, assuming it doesn't turn at all.
  • A full angle, assuming it makes one full turn.

So, the answer is "Null" or "Full."

FLAG

Which of the following shows a full angle?

a
b
c
d
e

What type of angle is $\angle BAC,$ shown in the figure above?

a
Full or Straight
b
Other
c
Right
d
Null or Full
e
Straight
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