independent practice
classify the angles as acute, obtuse, right or straight,
1) angle diagram acute
2) angle diagram ______
3) angle diagram ______
4) angle diagram ______
5) angle diagram ______
16) 180° ______
17) 18° ______
18) 90° ______
19) 110° ______
20) 167° ______

consider the figure below. complete each statement.
figure with lines ( l_1 ), ( l_2 ), angles ( a ), ( b ), ( c ), ( d ), ( e )
1. ( angle a ) and ( angle d ) are options: vertical angles, complimentary angles, supplementary angles, a linear pair
2. ( angle c ) and ( angle d ) are options: vertical angles, complimentary...

Question

independent practice
classify the angles as acute, obtuse, right or straight,
1) angle diagram acute
2) angle diagram ______
3) angle diagram ______
4) angle diagram ______
5) angle diagram ______
16) 180° ______
17) 18° ______
18) 90° ______
19) 110° ______
20) 167° ______

consider the figure below. complete each statement.
figure with lines ( l_1 ), ( l_2 ), angles ( a ), ( b ), ( c ), ( d ), ( e )
1. ( angle a ) and ( angle d ) are options: vertical angles, complimentary angles, supplementary angles, a linear pair
2. ( angle c ) and ( angle d ) are options: vertical angles, complimentary...

Accepted Answer

### Problem 16: Classify $ 180^\circ $ angle
# Explanation:
## Step1: Recall angle definitions
- Acute: $ 0^\circ < \theta < 90^\circ $
- Right: $ \theta = 90^\circ $
- Obtuse: $ 90^\circ < \theta < 180^\circ $
- Straight: $ \theta = 180^\circ $

## Step2: Match $ 180^\circ $ to definition
Since $ 180^\circ $ matches the straight angle definition.
# Answer: Straight

### Problem 17: Classify $ 18^\circ $ angle
# Explanation:
## Step1: Recall angle definitions
- Acute: $ 0^\circ < \theta < 90^\circ $
- Right: $ \theta = 90^\circ $
- Obtuse: $ 90^\circ < \theta < 180^\circ $
- Straight: $ \theta = 180^\circ $

## Step2: Match $ 18^\circ $ to definition
$ 18^\circ $ is between $ 0^\circ $ and $ 90^\circ $, so it is acute.
# Answer: Acute

### Problem 18: Classify $ 90^\circ $ angle
# Explanation:
## Step1: Recall angle definitions
- Acute: $ 0^\circ < \theta < 90^\circ $
- Right: $ \theta = 90^\circ $
- Obtuse: $ 90^\circ < \theta < 180^\circ $
- Straight: $ \theta = 180^\circ $

## Step2: Match $ 90^\circ $ to definition
$ 90^\circ $ matches the right angle definition.
# Answer: Right

### Problem 19: Classify $ 110^\circ $ angle
# Explanation:
## Step1: Recall angle definitions
- Acute: $ 0^\circ < \theta < 90^\circ $
- Right: $ \theta = 90^\circ $
- Obtuse: $ 90^\circ < \theta < 180^\circ $
- Straight: $ \theta = 180^\circ $

## Step2: Match $ 110^\circ $ to definition
$ 110^\circ $ is between $ 90^\circ $ and $ 180^\circ $, so it is obtuse.
# Answer: Obtuse

### Problem 20: Classify $ 167^\circ $ angle
# Explanation:
## Step1: Recall angle definitions
- Acute: $ 0^\circ < \theta < 90^\circ $
- Right: $ \theta = 90^\circ $
- Obtuse: $ 90^\circ < \theta < 180^\circ $
- Straight: $ \theta = 180^\circ $

## Step2: Match $ 167^\circ $ to definition
$ 167^\circ $ is between $ 90^\circ $ and $ 180^\circ $, so it is obtuse.
# Answer: Obtuse

### Problem 1 (Angle Relationship: $ \angle a $ and $ \angle d $)
# Explanation:
## Step1: Recall angle relationship definitions
- Vertical Angles: Opposite angles formed by intersecting lines, equal in measure.
- Complementary: Sum to $ 90^\circ $.
- Supplementary: Sum to $ 180^\circ $.
- Linear Pair: Adjacent, form a straight line (sum to $ 180^\circ $).

## Step2: Analyze $ \angle a $ and $ \angle d $
$ \angle a $ and $ \angle d $ are opposite angles formed by intersecting lines $ l_1 $ and $ l_2 $, so they are vertical angles.
# Answer: Vertical Angles

### Problem 2 (Angle Relationship: $ \angle c $ and $ \angle d $)
# Explanation:
## Step1: Recall angle relationship definitions
- Vertical Angles: Opposite angles formed by intersecting lines, equal in measure.
- Complementary: Sum to $ 90^\circ $.
- Supplementary: Sum to $ 180^\circ $ (if adjacent, linear pair).

## Step2: Analyze $ \angle c $ and $ \angle d $
$ \angle c $ and $ \angle d $ are adjacent and form a straight line (along $ l_2 $ and the other line), so they are a linear pair (supplementary, but linear pair is more specific here). Wait, actually, looking at the diagram, $ \angle c $ and $ \angle d $ are adjacent and form a right angle? Wait, no—wait, the diagram has a right angle? Wait, no, the lines: $ l_2 $ is horizontal, and the other line (with $ \angle c $ and $ \angle d $)—wait, maybe $ \angle c $ and $ \angle d $ are complementary? Wait, no, let's recheck. Wait, the options: "Vertical Angles", "Complimentary Angles" (typo for Complementary), etc. Wait, if $ \angle c $ and $ \angle d $ are adjacent and form a right angle (sum to $ 90^\circ $), then they are complementary. But from the diagram, if there's a right angle symbol (maybe $ \angle b $ is right? Wait, the diagram shows $ \angle b $ with a right angle? Wait, the user's diagram: $ l_1 $ and $ l_2 $, with $ \angle b $ maybe a right angle? Wait, maybe $ \angle c $ and $ \angle d $ are complementary. But let's assume: if $ \angle c + \angle d = 90^\circ $, then complementary. Alternatively, vertical angles? No, vertical angles are opposite. $ \angle c $ and $ \angle d $ are adjacent, so not vertical. So likely complementary (if they sum to $ 90^\circ $) or supplementary. Wait, the options include "Complimentary Angles" (complementary). So the answer is Complementary Angles (or Complimentary as per typo).
# Answer: Complimentary Angles (Complementary Angles)

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QUESTION IMAGE

Question

Explanation:

Problem 16: Classify \( 180^\circ \) angle

Step1: Recall angle definitions

Step2: Match \( 180^\circ \) to definition

Step1: Recall angle definitions

Step2: Match \( 18^\circ \) to definition

Step1: Recall angle definitions

Step2: Match \( 90^\circ \) to definition

Answer:

Problem 17: Classify \( 18^\circ \) angle