# 9.10.2. The Relation between Inscribed and Central Angles Subtended by the Same Arc

Given that , find the value of .

• A40
• B100
• C80
• D50

### Example

Given that , find the value of .

### Solution

The measure of an inscribed angle of a circle is half the measure of the central angle subtended by the same arc. This means that the measure of is half the measure of . First, use this fact to find the measure of in terms of as follows:

Since the measure of a central angle is equal to the measure of the arc that subtends it, the measure of arc is . Now extend radius so that it becomes diameter . There are in a semicircle, so the measure of arc is . Also, the measure of an inscribed angle is half the measure of the arc that subtends it. This means that the measure of is half the measure of arc . Next, use this fact to solve for the measure of in terms of .

The measure of is the same as the measure of , so the measure of is . Finally, use the fact that the sum of the measures of the interior angles of a triangle is to solve for .

0
correct
0
incorrect
0
skipped