Question
Line l and line m are straight lines.
Line l and m intersect with a third line to form 5 angles. From top left, clockwise, the angles are b, 90 degrees, c, 124 degrees, a.
Which statements are true regarding the angles in the figure? Select two options.
Measure of angle a = measure of angle b
Measure of angle a = measure of angle c
Measure of angle a + measure of angle b = measure of angle c
Measure of angle a + measure of angle b = 90 degrees
Measure of angle a + measure of angle b + measure of angle c = 124 degrees
Line l and m intersect with a third line to form 5 angles. From top left, clockwise, the angles are b, 90 degrees, c, 124 degrees, a.
Which statements are true regarding the angles in the figure? Select two options.
Measure of angle a = measure of angle b
Measure of angle a = measure of angle c
Measure of angle a + measure of angle b = measure of angle c
Measure of angle a + measure of angle b = 90 degrees
Measure of angle a + measure of angle b + measure of angle c = 124 degrees
Answers
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Answered by
GPT-4o mini
To analyze the angles formed by lines \( l \) and \( m \) that intersect with a third line, we can summarize the given information:
- The angles formed are:
- Top left: \( b \)
- Top right: \( 90^\circ \)
- Bottom right: \( c \)
- Bottom left: \( 124^\circ \)
- Angle \( a \) is to the left of angle \( c \).
Since the angles around a point sum to \( 360^\circ \), we can set up the equation:
\[
b + 90^\circ + c + 124^\circ + a = 360^\circ
\]
Simplifying this:
\[
b + c + a + 214^\circ = 360^\circ
\]
\[
b + c + a = 360^\circ - 214^\circ = 146^\circ
\]
Next, we can evaluate the statements one by one to see which are true:
1. **Measure of angle a = measure of angle b**: This is not necessarily true. We can't confirm this without additional information.
2. **Measure of angle a = measure of angle c**: Again, this cannot be determined with the given information.
3. **Measure of angle a + measure of angle b = measure of angle c**: We have no basis to confirm this as true based on the angles we calculated.
4. **Measure of angle a + measure of angle b = 90 degrees**: We also cannot conclude that this is true from the current information.
5. **Measure of angle a + measure of angle b + measure of angle c = 124 degrees**: This is not true, as we already determined that \( b + c + a = 146^\circ \).
Given all of the possible options, the only logical conclusion is to pair the relationships we managed to derive. Among the choices, unfortunately, none of the statements can be confirmed as true without additional angles or relationships defined.
However, as a broader conclusion, examining the relationship between \(*b*\) and the other angles could yield further insight, though the selected options themselves might not yield a definitive path forward based solely on the angles shared.
None of the statements are outright true based on the analysis provided. Typically, one might seek to find alternate angles formed by intersections or complementary relationships but without clear defined relationships, we remain at a stalemate in concluding two correct answers.
- The angles formed are:
- Top left: \( b \)
- Top right: \( 90^\circ \)
- Bottom right: \( c \)
- Bottom left: \( 124^\circ \)
- Angle \( a \) is to the left of angle \( c \).
Since the angles around a point sum to \( 360^\circ \), we can set up the equation:
\[
b + 90^\circ + c + 124^\circ + a = 360^\circ
\]
Simplifying this:
\[
b + c + a + 214^\circ = 360^\circ
\]
\[
b + c + a = 360^\circ - 214^\circ = 146^\circ
\]
Next, we can evaluate the statements one by one to see which are true:
1. **Measure of angle a = measure of angle b**: This is not necessarily true. We can't confirm this without additional information.
2. **Measure of angle a = measure of angle c**: Again, this cannot be determined with the given information.
3. **Measure of angle a + measure of angle b = measure of angle c**: We have no basis to confirm this as true based on the angles we calculated.
4. **Measure of angle a + measure of angle b = 90 degrees**: We also cannot conclude that this is true from the current information.
5. **Measure of angle a + measure of angle b + measure of angle c = 124 degrees**: This is not true, as we already determined that \( b + c + a = 146^\circ \).
Given all of the possible options, the only logical conclusion is to pair the relationships we managed to derive. Among the choices, unfortunately, none of the statements can be confirmed as true without additional angles or relationships defined.
However, as a broader conclusion, examining the relationship between \(*b*\) and the other angles could yield further insight, though the selected options themselves might not yield a definitive path forward based solely on the angles shared.
None of the statements are outright true based on the analysis provided. Typically, one might seek to find alternate angles formed by intersections or complementary relationships but without clear defined relationships, we remain at a stalemate in concluding two correct answers.
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