SOLUTION: Quadrilateral PQRS is inscribed in a circle. The ratio of m(angle)P to m(angle)R is 2:4. What is the m(angle)R? Four possible answers: A. 30 degrees B. 120 degrees C. 60 degree

Question 1159150: Quadrilateral PQRS is inscribed in a circle. The ratio of m(angle)P to m(angle)R is 2:4. What is the m(angle)R?
Four possible answers:
A. 30 degrees
B. 120 degrees
C. 60 degrees
D. Not here
Thank you :)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

For a quadrilateral inscribed in a circle, the sum of the measures of opposite angles is 180 degrees. Note that is because the two angles together cut off two arcs for which the sum of the measures is 360 degrees.

So angles P and R sum to 180 degrees; and the ratio is P:R = 2:4.

You can do the simple calculations to find the measure of angle R.

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You shouldn't need reassurance that 120 degrees is the right answer for the measure of angle R.

120 degrees for angle R means 60 degrees for angle P; and that makes P:R = 60:120 = 2:4.

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