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.

Question

What is an equation for these two adjacent angles?

(2 points)

Answer 1

To find an equation for the two adjacent angles described in your illustration, we need to understand the relationship between them.

The angle between the first ray (to the left) and the third ray (to the top right) is given as \( (2x + 3)^\circ \), and the angle between the second ray (to the right) and the third ray is given as \( (x - 6)^\circ \).

Since these two angles are adjacent and form a straight line with the third ray, their sum must equal \( 180^\circ \):

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

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