Question

A student inscribes a triangle inside a circle. The triangle divides the circle into arcs with the following measures: 46°, 102°, and 212°. What are the measures of the angles of the triangle?

Answer 1

To find the measures of the angles of the inscribed triangle, use the fact that an inscribed angle is half the measure of the central angle.

Step-by-step explanation:

To find the measures of the angles of the inscribed triangle, we can use the fact that an inscribed angle is half the measure of the central angle that intercepts the same arc. Let's call the angles of the triangle A, B, and C. We have the measures of the arcs: 46°, 102°, and 212°. So, we can say that A is half of 46°, B is half of 102°, and C is half of 212°. Therefore, the measures of the angles of the triangle are A = 23°, B = 51°, and C = 106°.

Answer 2

The angle of each arc is going to equal the measure of the angle opposite the arc... so the angles of the triangle will also be 46 degrees, 102 degrees, and 212 degrees.

(Look at one of the angles of the triangle and follow it as it opens up all the way to the other side of the circle and you'll see the equivalent arc)