Solution to QOTD 3/26/2020

For this question, you will have to apply the some properties of angles and arcs in circles. Here are a few of those that will help:

  1. The measure of an inscribed angle is 1/2 the measure of its intercepted arc;
  2. The measure of a central angle is equal to the measure of its intercepted arc;
  3. When an inscribed angle intercepts a diameter, the angle will be a right angle.

First, because we are given that <A is 30*, we know that the measure of Arc BD is 60*. (see property #1 above.) Therefore, the measure of <BCD is also 60*. (see property #2)

Next, <ABD intercepts the diameter of the circle, so, from property #3, <ABD is 90*.