Question

se the image to answer the question.

An illustration shows a horizontal line with arrows at both ends. Another line with arrows at both ends extends from top right to bottom left and intersects the horizontal line in the center. The intersecting line creates 4 angles. The angle at the top left is labeled x degrees. The angle at top right is labeled y degrees. The angles at bottom left and right below the horizontal line are not labeled.

What is the value of x if y°=71° ?

Answer 1

To solve the problem, we should use the properties of angles formed by intersecting lines. When two lines intersect, they create pairs of vertical angles that are equal and adjacent angles that are supplementary (i.e., they add up to 180 degrees).

In this case, we have:

- The angle at the top left labeled as \(x\) degrees.
- The angle at the top right labeled as \(y\) degrees, which is given as \(71°\).

Since angles \(x\) and \(y\) are adjacent angles formed by the intersection of the lines, their sum must equal \(180°\):

\[
x + y = 180°
\]

Substituting the value of \(y\):

\[
x + 71° = 180°
\]

Now, to find \(x\), we rearrange the equation:

\[
x = 180° - 71°
\]
\[
x = 109°
\]

Therefore, the value of \(x\) is \(109°\).