SOLUTION: In the diagram below, sécanos PT and PU have been drawn from exterior point P such that the four arcs intercepted have the following ratio of measurements: mRS:mST:mTU:mUR=1:4:4:3

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Question 1159927: In the diagram below, sécanos PT and PU have been drawn from exterior point P such that the four arcs intercepted have the following ratio of measurements: mRS:mST:mTU:mUR=1:4:4:3
a)What are the measures of each arc?
b)What is the measure of
c)Draw in UT. What is the measure of https://docs.google.com/document/d/15A1pLLRT4zMND-r6TmK0rvFKGFdbKkNtvs6tX4vQZjs/edit
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The four arcs together make the whole 360 degrees of the circle.

x%2B4x%2B4x%2B3x+=+360
12x+=+360
x+=+30

(a) The measures of the arcs are 30, 120, 120, and 90 degrees.

(b) The measure of angle P is half the difference between the measures of the two intercepted arcs: (1/2)(120-30) = 45 degrees.

(c) Angle PUT intercepts arc RST, which has measure 30+120 = 150 degrees. The measure of the angle is half the measure of the intercepted arc: 150/2 = 75 degrees.