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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
?

(1 point)

Answer 1

To find the measure of angle \( s \) (the angle between the second and third rays), we can use the information given about the three rays.

1. Let the angles be as follows:

   • The angle between the first ray and the second ray is \( 54^\circ \).
   • The angle between the first ray and the third ray is \( 80^\circ \).
   • We need to find the angle \( s \) between the second and third rays.

2. Since all angles are formed at the common origin, the sum of the angles around a point is \( 360^\circ \).

3. To find \( s \), we can use the relationship of the angles: \[ \text{Angle between the first ray and the second ray} + \text{Angle between the second ray and the third ray} + \text{Angle between the first ray and the third ray} = 180^\circ \]

4. Thus, we have: \[ 54^\circ + s + 80^\circ = 180^\circ \]

5. Combining the angles: \[ 134^\circ + s = 180^\circ \]

6. Solving for \( s \): \[ s = 180^\circ - 134^\circ \] \[ s = 46^\circ \]

Therefore, the measure of \( ∠s \) is \( 46^\circ \).