In the figure, angles b° – a°/2 and 2a° – 2b° must be positive. Hence, we have the inequalities, b – a/2 > 0
and 2a – 2b > 0.
Adding a/2 to both sides of first inequality and 2b to both sides of second inequality yields the following
two inequalities:
b > a/2
2a > 2b
Dividing the second inequality by 2 yields a > b.
Now, summing angles around point O to 360° yields a + (b – a/2) + (a/2 + 2b) + (2a – 2b) + (2a – b) = 360.
Simplifying this yields 5a = 360, and solving yields a = 360/5 = 72.
Substituting this value in the inequalities b > a/2 and a > b yields
b > a/2 = 72/2 = 36, and 72 > b
Combining the inequalities b > 36 and 72 > b yields 36 < b < 72. The only choice in this range is (C), so the answer is (C).