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 left 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 4 n plus 22 right parenthesis degrees. The angle between second and third rays is labeled as left parenthesis 8 n minus 10 right parenthesis degrees.

What is an accurate equation for the two adjacent angles?

(1 point)
Responses

(4n+22)°−(8n−10)°=180°
left parenthesis 4 n plus 22 right parenthesis degrees minus left parenthesis 8 n minus 10 right parenthesis degrees equals 180 degrees

(4n+22)°+(8n−10)°=180°
left parenthesis 4 n plus 22 right parenthesis degrees plus left parenthesis 8 n minus 10 right parenthesis degrees equals 180 degrees

(4n−8n)°−(22−10)°=180°
left parenthesis 4 n minus 8 n right parenthesis degrees minus left parenthesis 22 minus 10 right parenthesis degrees equals 180 degrees

(4n+8n)°+(22+10)°=180°

Answer 1

To find the correct equation for the two adjacent angles formed by the rays, we need to recognize that the angles are supplementary because they are adjacent and form a linear pair.

The angles are:

• The angle between the first ray and the third ray: \( (4n + 22)^\circ \)
• The angle between the second ray and the third ray: \( (8n - 10)^\circ \)

Since these two angles are adjacent and create a straight line (sum to 180 degrees), we can write the equation as follows:

\[ (4n + 22) + (8n - 10) = 180 \]

This simplifies to:

\[ (4n + 22) + (8n - 10) = 180 \]

Therefore, the accurate equation is:

(4n + 22)° + (8n - 10)° = 180°

Thus, the response is:

(4n + 22)° + (8n - 10)° = 180°