Question

categorization 1 point
classify each of the following angles as acute, right, obtuse or straight:
acute angles
no answers chosen
right angles

Explanation:

To solve this, we recall the definitions:

• Acute angle: Less than \( 90^\circ \) (and greater than \( 0^\circ \)).
• Right angle: Exactly \( 90^\circ \).
• Obtuse angle: Greater than \( 90^\circ \) but less than \( 180^\circ \).
• Straight angle: Exactly \( 180^\circ \).

Step 1: Identify Acute Angles

Check angles less than \( 90^\circ \):

• 3) \( 61^\circ \) ( \( 0 < 61 < 90 \) )
• 8) \( 54^\circ \) ( \( 0 < 54 < 90 \) )
• 10) \( 21^\circ \) ( \( 0 < 21 < 90 \) )
• 11) \( 37^\circ \) ( \( 0 < 37 < 90 \) )

Step 2: Identify Right Angles

Check angles equal to \( 90^\circ \):

• 1) \( 90^\circ \)
• 5) \( 90^\circ \)

Step 3: Identify Obtuse Angles

Check angles between \( 90^\circ \) and \( 180^\circ \):

• 2) \( 141^\circ \) ( \( 90 < 141 < 180 \) )
• 4) \( 138^\circ \) ( \( 90 < 138 < 180 \) )
• 6) \( 172^\circ \) ( \( 90 < 172 < 180 \) )
• 9) \( 106^\circ \) ( \( 90 < 106 < 180 \) )

Step 4: Identify Straight Angles

Check angles equal to \( 180^\circ \):

• 7) \( 180^\circ \)

Final Classification:

• Acute angles: 3, 8, 10, 11
• Right angles: 1, 5
• Obtuse angles: 2, 4, 6, 9
• Straight angle: 7

(If the question asks for acute angles specifically, the answer is: 3, 8, 10, 11)

Answer:

To solve this, we recall the definitions:

• Acute angle: Less than \( 90^\circ \) (and greater than \( 0^\circ \)).
• Right angle: Exactly \( 90^\circ \).
• Obtuse angle: Greater than \( 90^\circ \) but less than \( 180^\circ \).
• Straight angle: Exactly \( 180^\circ \).

Step 1: Identify Acute Angles

Check angles less than \( 90^\circ \):

• 3) \( 61^\circ \) ( \( 0 < 61 < 90 \) )
• 8) \( 54^\circ \) ( \( 0 < 54 < 90 \) )
• 10) \( 21^\circ \) ( \( 0 < 21 < 90 \) )
• 11) \( 37^\circ \) ( \( 0 < 37 < 90 \) )

Step 2: Identify Right Angles

Check angles equal to \( 90^\circ \):

• 1) \( 90^\circ \)
• 5) \( 90^\circ \)

Step 3: Identify Obtuse Angles

Check angles between \( 90^\circ \) and \( 180^\circ \):

• 2) \( 141^\circ \) ( \( 90 < 141 < 180 \) )
• 4) \( 138^\circ \) ( \( 90 < 138 < 180 \) )
• 6) \( 172^\circ \) ( \( 90 < 172 < 180 \) )
• 9) \( 106^\circ \) ( \( 90 < 106 < 180 \) )

Step 4: Identify Straight Angles

Check angles equal to \( 180^\circ \):

• 7) \( 180^\circ \)

Final Classification:

• Acute angles: 3, 8, 10, 11
• Right angles: 1, 5
• Obtuse angles: 2, 4, 6, 9
• Straight angle: 7

(If the question asks for acute angles specifically, the answer is: 3, 8, 10, 11)