Which is larger? The measure of a central angle of a circle that intercepts a 68 degrees arc or the measure an inscribed angle of a circle that intercepts a 68 degrees arc. Explain.

9514 1404 393

  the central angle

Step-by-step explanation:

The measure of the central angle is the same as that of the arc: 68°. The measure of the inscribed angle is half the measure of the arc: 68°/2 = 34°. The central angle is larger.

Additional comment

Consider the chord between the end points of the arc. Any inscribed angle whose vertex is on the long arc between the ends of the chord will have the same measure: 34°. If the vertex is moved off that long arc into the interior of the circle, the angle increases in size. When the vertex is at the center of the circle, the angle measure is the same as the arc measure: 68°. As the vertex approaches the chord, the measure of the angle increases. It becomes 180° when the vertex is on the chord, forming a straight angle.

The smallest angle that can be made with the chord ends and a vertex inside the circle is the inscribed angle. So, the central angle is larger.

step-by-step explanation:

what is the answer to this