Question
Find the measure of angle w.
Angle b and angle c are complementary angles. Write an equation that represents the relationship between angle b and angle c.
2 parallel lines cut by a transversal. The top intersection has a line segment extending vertically from the intersection of the transversal and the horizontal line. Clockwise from top left, the top intersection shows 5 angles labeled c, b, a, e, and d. Clockwise from top left, the bottom intersection shows 4 angles labeled x, w, z, and y.
Good work!
Angle e and angle w are supplementary angles. Write an equation that represents the relationship between angle e and angle w.
b+c=90
2 parallel lines cut by a transversal. The top intersection has a line segment extending vertically from the intersection of the transversal and the horizontal line. Clockwise from top left, the top intersection shows 5 angles labeled c, b, a, e, and d. Clockwise from top left, the bottom intersection shows 4 angles labeled x, w, z, and y.
Good work!
Angle e and angle c are vertical angles. Write an equation that represents the relationship between angle e and angle c.
b+c=90
e+w=180
2 parallel lines cut by a transversal. The top intersection has a line segment extending vertically from the intersection of the transversal and the horizontal line. Clockwise from top left, the top intersection shows 5 angles labeled c, b, a, e, and d. Clockwise from top left, the bottom intersection shows 4 angles labeled x, w, z, and y.
Angle b and angle c are complementary angles. Write an equation that represents the relationship between angle b and angle c.
2 parallel lines cut by a transversal. The top intersection has a line segment extending vertically from the intersection of the transversal and the horizontal line. Clockwise from top left, the top intersection shows 5 angles labeled c, b, a, e, and d. Clockwise from top left, the bottom intersection shows 4 angles labeled x, w, z, and y.
Good work!
Angle e and angle w are supplementary angles. Write an equation that represents the relationship between angle e and angle w.
b+c=90
2 parallel lines cut by a transversal. The top intersection has a line segment extending vertically from the intersection of the transversal and the horizontal line. Clockwise from top left, the top intersection shows 5 angles labeled c, b, a, e, and d. Clockwise from top left, the bottom intersection shows 4 angles labeled x, w, z, and y.
Good work!
Angle e and angle c are vertical angles. Write an equation that represents the relationship between angle e and angle c.
b+c=90
e+w=180
2 parallel lines cut by a transversal. The top intersection has a line segment extending vertically from the intersection of the transversal and the horizontal line. Clockwise from top left, the top intersection shows 5 angles labeled c, b, a, e, and d. Clockwise from top left, the bottom intersection shows 4 angles labeled x, w, z, and y.
Answers
GPT-4o mini
To summarize the relationships you provided among the angles and find the measure of angle \( w \), let's break down the information step by step.
1. **Complementary Angles**:
- Angles \( b \) and \( c \) are complementary. This means:
\[
b + c = 90^\circ
\]
2. **Supplementary Angles**:
- Angles \( e \) and \( w \) are supplementary. This means:
\[
e + w = 180^\circ
\]
3. **Vertical Angles**:
- Angles \( e \) and \( c \) are vertical angles, which means:
\[
e = c
\]
### Finding the Measure of Angle \( w \)
From the vertical angles relationship, we can substitute \( c \) in the complementary angles equation with \( e \):
\[
b + e = 90^\circ
\]
From here, we can express \( e \) in terms of \( b \):
\[
e = 90^\circ - b
\]
Now substituting \( e \) into the supplementary angles equation:
\[
(90^\circ - b) + w = 180^\circ
\]
Solving for \( w \):
\[
w = 180^\circ - (90^\circ - b)
\]
\[
w = 180^\circ - 90^\circ + b
\]
\[
w = 90^\circ + b
\]
### Summary of the Relationships:
1. \( b + c = 90^\circ \)
2. \( e + w = 180^\circ \)
3. \( e = c \)
4. \( w = 90^\circ + b \)
Now you can use any specific value for angle \( b \) to find the respective values for \( c \), \( e \), and \( w \).
1. **Complementary Angles**:
- Angles \( b \) and \( c \) are complementary. This means:
\[
b + c = 90^\circ
\]
2. **Supplementary Angles**:
- Angles \( e \) and \( w \) are supplementary. This means:
\[
e + w = 180^\circ
\]
3. **Vertical Angles**:
- Angles \( e \) and \( c \) are vertical angles, which means:
\[
e = c
\]
### Finding the Measure of Angle \( w \)
From the vertical angles relationship, we can substitute \( c \) in the complementary angles equation with \( e \):
\[
b + e = 90^\circ
\]
From here, we can express \( e \) in terms of \( b \):
\[
e = 90^\circ - b
\]
Now substituting \( e \) into the supplementary angles equation:
\[
(90^\circ - b) + w = 180^\circ
\]
Solving for \( w \):
\[
w = 180^\circ - (90^\circ - b)
\]
\[
w = 180^\circ - 90^\circ + b
\]
\[
w = 90^\circ + b
\]
### Summary of the Relationships:
1. \( b + c = 90^\circ \)
2. \( e + w = 180^\circ \)
3. \( e = c \)
4. \( w = 90^\circ + b \)
Now you can use any specific value for angle \( b \) to find the respective values for \( c \), \( e \), and \( w \).