Today’s SAT question of the day is a fun math question that reviews some geometry basics.  You’ll definitely need those basics for your test, so let’s give this one a try.

We are told that the radius of circle O is 5 and that the area of the shaded region is 20pi. X is what we are seeking.

Since the area of a circle is pi * the radius squared, we know that the whole circle’s area is 25pi. Let’s also remember that there are 360 degrees in a circle.To find the percent of the circle that is shaded, we can divide the area of the shaded part by the area of the whole circle. 20pi / 25pi = .8, or 80 percent.

80 percent of 360 is 288 degrees (.8 * 360 = 288). The shaded area accounts for 288 degrees, leaving 72 degrees for the central angle.  However, we are not trying to find the measure of the central angle; we need to find x.

Conveniently, the triangle that we are given is a right triangle.  Recalling that there are 180 degrees in a triangle and that a right angle measures 90 degrees, we can do the following to find x:

180 – 90 – 72 = x = 18 degrees.

This problem had a few steps to it, but as long as you remember your area formulas and your triangle and circle basics you should find problems like this one relatively painless.   Always remember to answer what the question is asking – 72 is probably a pretty popular answer choice for this problem, but it’s not x!