Use the image to answer the question.

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°
?

(1 point)

Answer 1

In the illustration described, you have two lines intersecting at a point, creating four angles. The pairs of opposite angles created by the intersection of the lines are equal, which means:

1. The angle \(x\) (top left) is equal to the angle at the bottom right.
2. The angle \(y\) (top right) is equal to the angle at the bottom left.

Since \(y = 71^\circ\), we have:

• The angle opposite \(y\) (which is the angle at the bottom left) is also \(71^\circ\).
• The angles \(x\) and \(y\) (or \(x\) and the angle at the bottom right) are supplementary because they form a linear pair along the horizontal line. This means:

\[ x + y = 180^\circ \]

Substituting \(y\) with \(71^\circ\):

\[ x + 71^\circ = 180^\circ \]

Now, solve for \(x\):

\[ x = 180^\circ - 71^\circ \] \[ x = 109^\circ \]

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