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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
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(1 point)
m∠s=

°
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Answer 1

To find the measure of angle ∠s, we can use the information given about the angles between the rays.

1. Let the angles be as follows:

   • ∠A = angle between the first ray and the second ray = 54 degrees
   • ∠B = angle between the first ray and the third ray = 80 degrees
   • ∠s = angle between the second ray and the third ray

2. By the property of angles around a point, we know that the sum of the angles around the common origin point (the point where the rays originate) should equal 360 degrees.

3. We can express the relationship as: \[ ∠A + ∠B + ∠s + 180° = 360° \] We add 180° because the second ray (which is inclined downward) and the third ray (which is also downward) essentially create a straight line with the angle ∠s, and we are considering angles around a point.

4. Rearranging the equation gives us: \[ ∠s = 360° - ∠A - ∠B - 180° \] \[ ∠s = 360° - 54° - 80° - 180° \]

5. Performing the calculations: \[ ∠s = 360° - 314° \] \[ ∠s = 46° \]

Thus, the measure of angle ∠s is 46 degrees.