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−

)°
+
°
=
°

Answer 1

To find the equation for the two adjacent angles, we first note that the two angles in question are the angle between the first ray and the third ray, which is given as \((5x - 25)°\), and the angle between the second ray and the third ray, which is given as \(55°\).

Since these two angles are adjacent and share a common ray (the third ray), they can be added together to form a straight angle, which measures \(180°\).

Thus, we can set up the equation:

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

This simplifies to:

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

Now, combining like terms gives:

\[ 5x + 30 = 180 \]

Therefore, the equation for the two adjacent angles is:

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

In response to your request to fill in the blanks:

\((5x - 25)° + 55° = 180°\)

Or,

\((x - 5)° + 55° = 180°\) if you were to express the first angle as \((x - 5)°\) to suggest another form, but for the specific given parameters:

\(5x - 25 + 55 = 180\) is correct.