Test 9 Section 5 - #18 (page 907)

They tell us there are 18 of each arc, and also that the circumference is 45, so the first thing I wanna do is write an equation.

18(2) + 18b = 45
36 + 18b = 45
18b = 9
b = 0.5

Note that since the diagram is drawn to scale, you can actually eyeball it and verify the answer you got with the math. It looks to me like 4 b's can fit into each arc marked 2, so 0.5 makes sense for b.

Set up a ratio now using [part]/[whole] = [part]/[whole]*.

[part of the circumference] = 0.5
[whole circumference] = 45

[degree measure of our arc] = x°
[degree measure of whole circle] = 360°

0.5/45 = x°/360°
180° = 45x° (cross multiply)
x° = 4°

The answer is (A), 4°.

We can verify this with everything else we know, just to make sure. Because we figured out before that 4 b's go into one of the bigger arcs, we know the bigger arcs must be 16°. There are 18 of each size arc. 18x16° = 288°, and 18x4° = 72°. 72°+288° = 360°. Done.

* TONS of circle questions on the SAT can be solved using this ratio, which can take the general form:


or, more usefully: