section 3: angle relationships
type of angle relationship | drawing | characteristics
complementary angles | drawing with 52° and 38° | two angles that add up to 90°
supplementary angles | drawing with 128° and 52° | two angles that add up to 180°

section 4: practice
name each relationship below.
diagrams numbered 1 (180°), 2, 3 (60° and 30°), 4 (right angle), 5 (45° and 135°), 6 (perpendicular lines), 7, 8 (35°), 9 (115°), 10 (cube), 11 (250°)
word bank: acute angle, complementary angles, intersecting lines, obtuse angle, parallel lines, perpendicular lines, reflex angle, right angle, skew lines, straight angle

Question

section 4: practice
name each relationship below.
diagrams numbered 1 (180°), 2, 3 (60° and 30°), 4 (right angle), 5 (45° and 135°), 6 (perpendicular lines), 7, 8 (35°), 9 (115°), 10 (cube), 11 (250°)
word bank: acute angle, complementary angles, intersecting lines, obtuse angle, parallel lines, perpendicular lines, reflex angle, right angle, skew lines, straight angle

Accepted Answer

### Problem 1 (Angle with $180^\circ$)
# Explanation:
## Step1: Identify the angle type.
A straight angle is defined as an angle that measures $180^\circ$, forming a straight line. The given angle here is $180^\circ$, so we match it to the "straight angle" from the word bank.
# Answer:
straight angle

### Problem 2 (Two parallel - looking lines)
# Explanation:
## Step1: Analyze the line relationship.
Parallel lines are lines in a plane that do not meet; they are always the same distance apart. The two lines in this problem appear to be parallel (they have the same direction and don't intersect), so we use the "parallel lines" from the word bank.
# Answer:
parallel lines

### Problem 3 (Angles $60^\circ$ and $30^\circ$)
# Explanation:
## Step1: Calculate the sum of angles.
We add the two angles: $60^\circ+ 30^\circ=90^\circ$.
## Step2: Identify the angle relationship.
Complementary angles are two angles whose sum is $90^\circ$. Since $60^\circ + 30^\circ=90^\circ$, the relationship is complementary angles.
# Answer:
complementary angles

### Problem 4 (Right - angled symbol)
# Explanation:
## Step1: Recognize the angle type.
A right angle is an angle of exactly $90^\circ$, and the symbol in the diagram (the square corner) indicates a right angle. So we use "right angle" from the word bank.
# Answer:
right angle

### Problem 5 (Angles $45^\circ$ and $135^\circ$)
# Explanation:
## Step1: Calculate the sum of angles.
We add the two angles: $45^\circ+135^\circ = 180^\circ$.
## Step2: Identify the angle relationship.
Supplementary angles are two angles whose sum is $180^\circ$. Since $45^\circ+135^\circ = 180^\circ$, the relationship is supplementary angles.
# Answer:
supplementary angles

### Problem 6 (Perpendicular - looking lines)
# Explanation:
## Step1: Analyze the line relationship.
Perpendicular lines are lines that intersect at a right angle ( $90^\circ$ ). The lines in this diagram have a right - angled intersection, so we use "perpendicular lines" from the word bank.
# Answer:
perpendicular lines

### Problem 7 (Intersecting lines)
# Explanation:
## Step1: Analyze the line relationship.
Intersecting lines are lines that cross each other at a point. The two lines in this diagram cross each other, so we use "intersecting lines" from the word bank.
# Answer:
intersecting lines

### Problem 8 (Angle of $35^\circ$)
# Explanation:
## Step1: Identify the angle type.
An acute angle is an angle that measures less than $90^\circ$. Since $35^\circ<90^\circ$, the angle is an acute angle.
# Answer:
acute angle

### Problem 9 (Angle of $115^\circ$)
# Explanation:
## Step1: Identify the angle type.
An obtuse angle is an angle that measures greater than $90^\circ$ but less than $180^\circ$. Since $90^\circ < 115^\circ<180^\circ$, the angle is an obtuse angle.
# Answer:
obtuse angle

### Problem 10 (Skew lines in a cube)
# Explanation:
## Step1: Analyze the line relationship.
Skew lines are lines that are not parallel and do not intersect, and they lie in different planes. In a cube, the lines shown (e.g., a vertical line on the front face and a horizontal line on the top face that don't intersect and aren't parallel) are skew lines. So we use "skew lines" from the word bank.
# Answer:
skew lines

### Problem 11 (Angle of $250^\circ$)
# Explanation:
## Step1: Identify the angle type.
A reflex angle is an angle that measures greater than $180^\circ$ but less than $360^\circ$. Since $180^\circ<250^\circ < 360^\circ$, the angle is a reflex angle.
# Answer:
reflex angle

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1 (Angle with \(180^\circ\))

Step1: Identify the angle type.

Step1: Analyze the line relationship.

Step1: Calculate the sum of angles.

Step2: Identify the angle relationship.

Answer:

Problem 2 (Two parallel - looking lines)