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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)
m∠s=

°er

Answer 1

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

1. Let the angles be defined as follows:

   • \( m∠A = 80° \) (angle between the first and the third rays)
   • \( m∠B = 54° \) (angle between the first and second rays)
   • \( m∠s \) = angle between the second and third rays.

2. The three angles \( A \), \( B \), and \( s \) form a circle (360 degrees) around the common origin point. Therefore, we can express the relationship between these angles as: \[ m∠A + m∠B + m∠s = 360° \]

3. Substituting the known values: \[ 80° + 54° + m∠s = 360° \]

4. Now, combine the known angles: \[ 134° + m∠s = 360° \]

5. To find \( m∠s \), subtract 134° from 360°: \[ m∠s = 360° - 134° \] \[ m∠s = 226° \]

So, the measure of \( ∠s \) is \( 226° \).