Use the image to answer the 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−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+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°

1 answer

To determine the equation representing the relationship between the two adjacent angles mentioned, we need to understand that these angles are supplementary, meaning they add up to 180 degrees.

  1. The angle between the first ray and the third ray is given as \((4n + 22)^\circ\).
  2. The angle between the second ray and the third ray is given as \((8n - 10)^\circ\).

Since these angles are adjacent and form a linear pair, we can express their relationship with the equation:

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

So, the correct response is:

(4n + 22)° + (8n − 10)° = 180°
\[ \text{left parenthesis 4 n plus 22 right parenthesis degrees plus left parenthesis 8 n minus 10 right parenthesis degrees equals 180 degrees} \]