Use the image to answer the question.

Question

An illustration shows three rays from a common vertex with labeled angles. The first ray is inclined to the horizontal left of the common vertex with an arrow at the end. The second ray is inclined to the horizontal right of the common vertex with an arrow at the end. The third ray is to the top right of the common vertex with an arrow at the end. It is between the other two rays. The angle between the first and the third rays is labeled as left parenthesis 5 x minus 25 right parenthesis degrees. The angle between the second and third rays as labeled as 55 degrees.

Write an equation for the two adjacent angles.

(2 points)
(
x−

)°
+
°
=
°
Remaining Attempts : 3

Answer 1

To write the equation for the two adjacent angles, you have the following information:

1. The angle between the first ray and the third ray is given as \( (5x - 25)^\circ \).
2. The angle between the second ray and the third ray is given as \( 55^\circ \).

Since these two angles are adjacent and lie on a straight line around the common vertex, their sum must equal \( 180^\circ \).

Thus, the equation can be set up as:

\[ (5x - 25) + 55 = 180 \]

After simplification, this equation represents the relationship between the two adjacent angles.