Find the measure of <RUS.
The diagram shows line P U T and 3 rays from point U: ray U Q, ray U R, and ray U S. The line and rays create the following angles. Angle P U Q is 39 degrees. Angle QUR is 23 degrees. Angle R U S is not given. Angle S U T is 28 degrees.
A)62
B)80
C)90
D)67
To find the measure of angle RUS, we can use the fact that the angles around a point add up to 360 degrees.
First, we know that angle PUQ is 39 degrees and angle QUR is 23 degrees. Since these angles are adjacent and on the same line, they form a straight angle, which measures 180 degrees. Therefore, angle RUQ is 180 - (39 + 23) = 118 degrees.
Next, we know that angle SUT is 28 degrees. Since this angle is adjacent and on the same line as angle RUS, they also form a straight angle. Therefore, angle RUS is 180 - 28 = 152 degrees.
Therefore, the measure of angle RUS is 152 degrees.
The answer is not given in the options provided.