7 In the given figure, O is the centre of the circle, ∠AOB = 600 and ∠CDB= 900. Find ∠OBC

To find ∠OBC, we can use the properties of angles in a circle.

Step 1: Recall that the measure of an angle formed by two radii of a circle is equal to half the measure of the intercepted arc.

Step 2: In this case, ∠AOB is formed by radii OA and OB, and its measure is given as 600. Therefore, the intercepted arc AB has a measure of 2 * 600 = 1200.

Step 3: Since ∠CDB is a right angle (900), the intercepted arc CD is a semicircle, which has a measure of 180 degrees.

Step 4: Now, we can find the measure of the arc BC by subtracting the measures of arcs AB and CD from the total measure of a circle, which is 360 degrees. So, arc BC = 360 - 1200 - 180 = -1020 degrees.

Step 5: However, angles cannot have negative measures, so we need to find the equivalent positive measure of arc BC. To do this, we add 360 degrees to -1020 degrees, which gives us 360 + (-1020) = -660 degrees.

Step 6: Finally, we can find the measure of ∠OBC by dividing the measure of arc BC by 2, since it is formed by radii OB and OC. So, ∠OBC = (-660) / 2 = -330 degrees.

Therefore, the measure of ∠OBC is -330 degrees.