Question

In the figure, point $O$ is the center of the circle, the measure of angle $RTB$ is $28$ degrees, and the measure of angle $ROB$ is three times the measure of angle $SOT$. What is the measure of minor arc $RS$, in degrees

Answer 1

To find the measure of minor arc RS, we need to determine the measure of angle SOT. Since angle RTB is given as 28 degrees, and angle ROB is three times the measure of angle SOT, we can set up an equation to solve for the measure of minor arc RS.

Step-by-step explanation:

To find the measure of minor arc RS, we need to determine the measure of angle SOT.

Since angle RTB is given as 28 degrees, and angle ROB is three times the measure of angle SOT, we can set up the equation 28 + 3x = 360, where x is the measure of angle SOT.

Solving this equation, we find that x = 104 degrees. Since angles SOT and ROB are vertical angles, they have the same measure.

Therefore, the measure of minor arc RS is equal to twice the measure of angle SOT, which is 2 * 104 = 208 degrees.