Solve Equations with Vertical Angles Practice

Question

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Question
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An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.

m∠1=125°
and m∠4=(x+35)°


What equation will solve for x
?

Answer 1

To find the value of \( x \) using the relationship between vertical angles, we can examine the angles given in the problem.

We know that vertical angles are equal. In this case, angles \( \angle 1 \) and \( \angle 4 \) are vertical angles, so:

\[ m\angle 1 = m\angle 4 \]

Given that \( m\angle 1 = 125^\circ \) and \( m\angle 4 = (x + 35)^\circ \), we can set up the equation:

\[ 125 = x + 35 \]

Now, this equation will help us solve for \( x \). Thus, the equation that will solve for \( x \) is:

\[ x + 35 = 125 \]