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Points P, Q, and R lie on the circumfere...

Points P, Q, and R lie on the circumference of the circle centered at O. If `angle OPQ` measures `x^(@)` and `angle QRO` measures `y^(@)`, what is the measure of `angle POR` in terms of x and y ?

A

`(360+x+y)^(@)`

B

`(360-x-y)^(@)`

C

`(360-2x-2y)^(@)`

D

`(180+x+y)^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
As is so often true when circles are combined with other figures, the key to solving this question is to draw in a radius :

All the radii of a circle are equal, so within each of the two triangles you just created, the angles opposite the radii are equal :

Now that you know two angles in each triangle, you can figure out the third :

The angle you're looking for is `(180-2x)^(@)+(180-2y)^(@)=(360-2x-2y)^(@)`.
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