Question
In the diagram, given m ∥ m, m∠8 = 2x - 1 and m∠1 = 115. What is the value of x?
Answers
Answered by
GPT-4o mini
To solve for \( x \) in the given situation involving parallel lines, we will use the properties of angles formed by a transversal.
Since \( m \) and \( m \) are parallel lines, \( m\angle 1 \) and \( m\angle 8 \) are corresponding angles. Their measures are equal. Thus, we can set up the equation:
\[
m\angle 1 = m\angle 8
\]
Given \( m\angle 1 = 115^\circ \) and \( m\angle 8 = 2x - 1 \), we can substitute these values into the equation:
\[
115 = 2x - 1
\]
Next, we will solve for \( x \).
1. Add \( 1 \) to both sides of the equation:
\[
115 + 1 = 2x
\]
\[
116 = 2x
\]
2. Now divide both sides by \( 2 \):
\[
x = \frac{116}{2}
\]
\[
x = 58
\]
Thus, the value of \( x \) is
\[
\boxed{58}
\]
Since \( m \) and \( m \) are parallel lines, \( m\angle 1 \) and \( m\angle 8 \) are corresponding angles. Their measures are equal. Thus, we can set up the equation:
\[
m\angle 1 = m\angle 8
\]
Given \( m\angle 1 = 115^\circ \) and \( m\angle 8 = 2x - 1 \), we can substitute these values into the equation:
\[
115 = 2x - 1
\]
Next, we will solve for \( x \).
1. Add \( 1 \) to both sides of the equation:
\[
115 + 1 = 2x
\]
\[
116 = 2x
\]
2. Now divide both sides by \( 2 \):
\[
x = \frac{116}{2}
\]
\[
x = 58
\]
Thus, the value of \( x \) is
\[
\boxed{58}
\]
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