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 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°
1 answer
The two angles that are adjacent and form a straight line at the common vertex must sum up to 180 degrees. According to the given labels:
Thus, the correct equation for the two adjacent angles is:
\[ (4n + 22)^\circ + (8n - 10)^\circ = 180^\circ \]
So, the answer is:
(4n + 22)° + (8n − 10)° = 180°
