Use the image to answer the question.

Question

An illustration shows three rays from a common origin point. The first ray is inclined to the top left of the common origin with an arrow at the end. The second ray is also inclined to the bottom left from the common origin with an arrow at the end. The second ray is below the first ray. The third ray is to the bottom left of the common origin with an arrow at the end. The third ray is below the second ray. The angle between the first and the third rays is labeled as 80 degrees. The angle between second and third rays is labeled as s degrees. The angle between first and second rays is labeled as 54 degrees.

What is the measure of ∠s
?

Answer 1

To find the measure of angle \( s \), we can use the information provided about the angles between the rays.

1. Identify the angles:

   • Let \( \alpha \) be the angle between the first ray and the second ray, which is given as \( \alpha = 54^\circ \).
   • Let \( \beta \) be the angle between the first ray and the third ray, which is given as \( \beta = 80^\circ \).
   • Let \( s \) be the angle between the second ray and the third ray.

2. Visualize the angles:

   • The angles sum around the common origin point.
   • The angle between the first and second rays is \( 54^\circ \).
   • The angle between the first ray and the third ray is \( 80^\circ \).
   • The angles around the origin must sum to \( 360^\circ \).

3. Set up the equation using angle sums:

   • Since we are interested in the angle between the second and third rays, we have the relationship: \[ s = 360^\circ - (\alpha + \beta) \]

4. Substitute the known angles: \[ s = 360^\circ - (54^\circ + 80^\circ) \]

5. Calculate: \[ s = 360^\circ - 134^\circ = 226^\circ \]

Thus, the measure of angle \( s \) is \( 226^\circ \).