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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 are all the angle mesurements

Answer 1

To find the angle measurements given in the description of the rays, we can use the information we have about the angles between them.

1. Let’s label the rays:

   • Ray 1 (top left)
   • Ray 2 (bottom left, below Ray 1)
   • Ray 3 (bottom left, below Ray 2)

2. Given angles:

   • Angle between Ray 1 and Ray 2 = 54 degrees (let’s call this angle A)
   • Angle between Ray 1 and Ray 3 = 80 degrees (let’s call this angle B)
   • Angle between Ray 2 and Ray 3 = s degrees (let’s call this angle C)

3. Understanding the angles: Since Ray 1 is the topmost ray and Ray 3 is the bottommost ray, we can find angle C using the relationship between the angles.

For Ray 1 and Ray 2:

• The angle between Ray 1 and Ray 2 (A) is given as 54 degrees.

For Ray 1 and Ray 3:

• The angle between Ray 1 and Ray 3 (B) is given as 80 degrees.

Ray 2 and Ray 3 make a triangle with the angle measurements around Ray 1. Therefore, we can find angle C (s) using the following relationship:

Sum of angles around point = 360 degrees.

From Ray 1: \[ A + B + C = 180 \text{ degrees} \ 54 + 80 + C = 180 \ C = 180 - 134 \ C = 46 \text{ degrees} \]

4. Final Measurements:

• Angle between Ray 1 and Ray 2 (A) = 54 degrees
• Angle between Ray 1 and Ray 3 (B) = 80 degrees
• Angle between Ray 2 and Ray 3 (C/s) = 46 degrees

So, the angle measurements are:

• Angle A = 54 degrees
• Angle B = 80 degrees
• Angle C (s) = 46 degrees