Proofs About Angles Practice

Question

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Question
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Two parallel, inclined lines labeled as m and n are separated by a distance. A diagonal line labeled as t intersects m and n at a bottom left to top right incline.

In the diagram, given m∥n
, m∠8=2x−1
and m∠1=115
. What is the value of x?

(1 point)
x=

Answer 1

To find the value of \( x \), we need to recognize the relationships between the angles in the given problem. Since lines \( m \) and \( n \) are parallel and line \( t \) is a transversal line, we can use angle relationships to solve for \( x \).

From the information provided:

• \( m \angle 8 = 2x - 1 \)
• \( m \angle 1 = 115^\circ \)

Since lines \( m \) and \( n \) are parallel, angles \( \angle 1 \) and \( \angle 8 \) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. Therefore:

\[ m \angle 8 = m \angle 1 \]

Substituting the given values into the equation:

\[ 2x - 1 = 115 \]

Now, solve for \( x \):

1. Add 1 to both sides: \[ 2x = 115 + 1 \] \[ 2x = 116 \]

2. Divide both sides by 2: \[ x = \frac{116}{2} \] \[ x = 58 \]

Thus, the value of \( x \) is \( \boxed{58} \).