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 for the two adjacent angles, we can set up the equation based on the information provided:

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

Since these two angles are adjacent and form a straight line when added together, their sum is equal to \(180^\circ\).

Therefore, we can write the equation as:

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

Now we can fill in the blanks:

• The first angle is \( (2x + 3)^\circ \).
• The second angle is \( (x - 6)^\circ \).
• The sum of both angles is \( 180^\circ \).

So the answer is:

(2x + 3)° + (x - 6)° = 180°.