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 2 x plus 3 right parenthesis degrees. The angle between the second and third rays is labeled as left parenthesis x minus 6 right parenthesis degrees.

What is an equation for these two adjacent angles?

(2 points)
(
x+
)°
+ (x−
)°
=
°

Answer 1

To find the equation involving the two adjacent angles based on the description provided, we have:

1. The angle between the first and third rays is labeled as \( (2x + 3)^\circ \).
2. The angle between the second and third rays is labeled as \( (x - 6)^\circ \).

Since these two angles are adjacent and together form a straight line, the sum of these angles should equal \( 180^\circ \).

Thus, we can write the equation as:

\[ (2x + 3) + (x - 6) = 180 \]

Now you can simplify the equation:

\[ 2x + 3 + x - 6 = 180 \] \[ 3x - 3 = 180 \]

This is the equation that represents the relationship between the two adjacent angles.