Marcel is designing a circular necklace that will consist of 4 sections, each with a different color of plastic. Determine how he needs to cut the plastic by finding the measures of the angles.
Answers
Answer:
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Answer:
Angle 1 = 83 degrees
Angle 2 = 97 degrees
Step-by-step explanation:
According to the attachment that I have (hopefully that's the one the question is related to), lets just say the arc with the angle 112 degrees will be arc 1 and the arc with the angle 54 degrees will be arc 3.
So (if you don't want to read that):
Arc 112 = Arc 1
Arc 54 = Arc 3
(this is just a heads up btw just to make it simpler for me to call them during the explanation)
To find angle 1:
1) Find the angle measure of angle 1 using the Angle formed by two chords theorem.
1a) The Angle formed by two chords theorem says: If two chords intersect within a circle, then the measure of each pair of vertical angles formed is equal to one-half the sum of the measures of their intercepted arcs.
2) So: arc 1(1/2) + arc 3(1/2) = angle 1
2a) 112(1/2) + 54(1/2) = angle 1
2b) 56 + 27 = angle 1
Therefore, angle 1 is 83 degrees.
To find angle 2:
1) Find angle 2 using the Supplementary Theorem(?). (Sorry forgot what it was called.)
1a) You know that supplementary angles means that the two angles (created by two perpendicular lines) that are adjacent to each other added up together will equal to 180 degrees.
2) Since angle 1 + angle 2 = 180 degrees
2a) 180 - angle 1 = angle 2
2b) 180 - 83 = angle 2
Therefore, angle 2 is 97 degrees.
Hopefully this helped! If not, please ask me more questions! I'm sorry if this was not the answer you were looking for!!
