Question

1. The measure of arc YX is 56 degrees. Find the measure of angle STY.

Answer 1

To find the measure of angle STY, we must first find the measure of angle XYT. Since arc YX is 56 degrees, we know that angle XYT is half of that, which is 28 degrees.

Angle STY is an inscribed angle that intercepts arc XY, so its measure is half of the measure of the central angle that intercepts the same arc. Since angle XYT intercepts the same arc, we can find the measure of the central angle by adding the measure of angle XYT and angle XYT, which is 56 degrees.

So, the measure of angle STY is half of 56 degrees, which is 28 degrees.