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.

Question

What is an accurate equation for the two adjacent angles?

(1 point)
Responses

(4n+8n)°+(22+10)°=180°
left parenthesis 4 n plus 8 n right parenthesis degrees plus left parenthesis 22 plus 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+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−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
Remaining Attempts : 1

Answer 1

To find the correct equation for the two adjacent angles, we need to identify how they relate to one another. The angles between the rays are the following:

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

Since these two angles are adjacent (they share a ray and together they form a straight line), they must sum up to \(180^\circ\).

The accurate equation is:

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

So, the correct response is:

(4n+22)°+(8n−10)°=180°