PR is a diameter of ⊙O and mRW =55.find: f.mEWR please help me answer this question
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PR is a diameter of ⊙O and mRW =55.find: f.mEWR please help me answer this question
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Answer:
To find the measure of angle EWR, we can use the following facts:
- PR is a diameter of the circle, so it passes through the center O and divides the circle into two semicircles.
- The measure of an angle inscribed in a semicircle is 90 degrees, so mZPRW = 90 and mZWER = 90.
- The sum of the measures of the angles in a triangle is 180 degrees, so mZRPW + mZPRW + mRW = 180 and mZWER + mZREW + mEWR = 180.
Using these facts, we can solve for mEWR by substituting the given values and simplifying:
mEWR = 180 - mZWER - mZREW
mEWR = 180 - 90 - (180 - mZRPW - mRW)
mEWR = 90 - mZRPW - mRW
mEWR = 90 - (90 - mRW) - mRW
mEWR = 2mRW - 90
mEWR = 2(55) - 90
mEWR = 20
Therefore, the measure of angle EWR is 20 degrees.