Question

What is the​ measure, in​ degrees, of the highlighted​ angle?
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x y graph
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Part 1
The measure of the highlighted angle is
  
enter your response here degrees.
​(Type an integer or a​ decimal.)

Answer 1

I can’t see the graph from your text. Please either upload the image or tell me the coordinates/description of the highlighted ray (for example: the ray goes from the origin through the point (4,8) or the ray makes slope 1/2, etc.).

If you want to compute it yourself, here are the steps:

- If the highlighted ray goes from the origin through a point (x,y) with x>0, the angle θ measured counterclockwise from the positive x-axis is
θ = arctan(y/x) (in degrees).
- If x<0 you must add 180° to arctan(y/x) (or use your calculator’s atan2(y,x) function) to get the correct quadrant.
- If x=0 and y>0, θ = 90°; if x=0 and y<0, θ = 270°.
- On a calculator use the inverse tangent (tan^-1 or atan) and make sure the calculator is set to DEGREES.

Examples:
- Through (8,4): θ = arctan(4/8) = arctan(0.5) ≈ 26.565°.
- Through (4,8): θ = arctan(8/4) = arctan(2) ≈ 63.435°.

Send the image or the point/slope and I’ll compute the exact value.