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−
)°
=
°
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Answer 1

To form an equation for the two adjacent angles, we can use the information given about their measurements:

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

Since these two angles are adjacent and together they form a straight line, we can express this relationship with the equation:

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

This is because the sum of the angles on a straight line equals \( 180^\circ \).

So, the equation for the two adjacent angles can be summarized as:

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