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Geometry and Measurement

Geometry Student-Produced Response

If the difference between the measures of two supplementary angles is \(80^\circ,\) what is the measure of the bigger angle? (Disregard the degree symbol when entering your answer.)

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In the figure above, \(CA = AF, BD = 15,\) and \(FD = 3.\) What is the value of \(CB?\)

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In the diagram above, the pattern is to be repeated until \(15\) squares, each with side \(s,\) fit on \(\overline{AB}.\) The area of all squares is \(M\) and if \(\overline{AB}\) is removed, the length of the remaining curve is \(N.\) If \(s\) is a positive integer, for how many values of \(s\) will \(M < N?\)

The sum of the interior angles of a certain convex polygon is \(19\) times the sum of its exterior angles. How many sides does the polygon have?

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The two circles shown above are concentric. If the distance between them is \(x=2\), and the bigger circle has area \(361\pi,\) what is the radius of the smaller circle?

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