Introduction

We categorize angles that are not right, straight, or full into three groups.

  • An acute angle has a measure between 0^\circ and 90^\circ\mathbin{:}

  • An obtuse angle has a measure between 90^\circ and 180^\circ\mathbin{:}

  • Angles whose measure is between 180^\circ and 360^\circ are called reflex angles.
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Example: Identifying Acute Angles

Which of the following shows an acute angle \angle CDE?

EXPLANATION

Remember that an acute angle has a measure between 0^\circ and 90^\circ. Therefore, the correct diagram is the following:

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Practice: Identifying Acute Angles

Which of the following shows an acute angle $\angle ABC?$

a
b
c
d
e
Practice: Identifying Acute Angles

Which of the following shows an acute angle $\angle PQR?$

a
b
c
d
e
Example: Identifying Obtuse Angles

Which of the following shows an obtuse angle \angle ABC?

EXPLANATION

Remember that an obtuse angle has a measure between 90^\circ and 180^\circ. Therefore, the correct diagram is the following:

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Practice: Identifying Obtuse Angles

Which of the following shows an obtuse angle $\angle ABC?$

a
b
c
d
e
Practice: Identifying Obtuse Angles

Which of the following shows an obtuse angle $\angle PQR?$

a
b
c
d
e
Example: Identifying Reflex Angles

Which of the following shows a reflex angle \angle CDE?

EXPLANATION

Remember that a reflex angle has a measure between 180^\circ and 360^\circ. Therefore, the correct diagram is the following:

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Practice: Identifying Reflex Angles

Which of the following shows a reflex angle $\angle ABC?$

a
b
c
d
e
Practice: Identifying Reflex Angles

Which of the following shows a reflex angle $\angle STU?$

a
b
c
d
e
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