Use 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.
Use the relationship between supplementary angles to determine the value of y° if x°=125° .
(1 point)
Responses
55°
55 degrees
305°
305 degrees
35°
35 degrees
125°
Since the intersecting line creates a straight line with the horizontal line, the angle at the top right and the angle at the bottom left will be supplementary. This means that the sum of their measures is 180°.
Therefore, we can set up the equation: y + angle at bottom left = 180°.
Since the angle at bottom left is not labeled, we can denote it as z°.
We can rewrite the equation as: y + z = 180°.
Given that x° = 125°, we know that the angle at the top left and the angle at the bottom right are also supplementary. So, we can set up the equation: x + angle at bottom right = 180°.
Since the angle at bottom right is not labeled, we can denote it as w°.
We can rewrite the equation as: 125° + w = 180°.
From the information given, we know that the angle at the top left and the angle at the top right are adjacent vertical angles. Therefore, they are congruent.
So, x° = y°. From the given information, we have x° = 125°, so y° = 125°.
Since y + z = 180°, and we know that y° = 125°, we can substitute 125° for y in the equation.
125° + z = 180°
Now, we can solve for z:
z = 180° - 125°
z = 55°
Therefore, the value of y° in this case is 125°.