Question

Use the image to answer the question.

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
?

(1 point)
x°+__ °=__°

Answer 1

To solve for \( x \) using the angles provided, we can leverage the fact that the angles formed by a transversal cutting through parallel lines have specific relationships.

Given that:
- \( m \angle 1 = 125° \)
- \( m \angle 4 = (x + 35)° \)

Angles 1 and 4 are corresponding angles because they are positioned relative to the same line (the slanting line) and fall between the two parallel lines. Since corresponding angles are equal when the lines are parallel, we can set up the following equation:

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

Substituting the values we have:

\[
125° = (x + 35)°
\]

To isolate \( x \), subtract 35° from both sides:

\[
125° - 35° = x
\]

This simplifies to:

\[
90° = x
\]

Now, rewriting this in the form of \( x° + __ ° = __° \):

We have:

\[
x + 35 = 125
\]

Thus, the equation that will solve for \( x \) can be written as:

\[
x° + 35° = 125°
\]

So, filling in the blanks:

\( x° + 35° = 125° \)