If O is the center of the circle above, what fraction…
In solving this problem there are three angle rules that we must consider.
1) A circle measures a total of 360 degrees.
2) A straight angle measures 180 degrees.
3) Vertical angles, angles that are directly opposite one another, are always equal.
To solve, we can draw out a quick diagram of just the angles:
Based on the angles we created, we know two important pieces of information:
1) angle A and 150 degrees sum to 180 degrees because they form a straight angle. Thus, angle A = 30 degrees.
2) angle A = angle B because they are vertical angles. Thus angle B = 30 degrees.
With this information we see that the shaded region represents 60 out of 360 degrees of the circle, or 60/360 = 1/6.