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 82 degrees. Angle Q U R is 24 degrees. Angle R U S is not given. Angle S U T is 51 degrees. Angle P U T includes all angles given.
A) 24
B)15
C)23
D)33
To find the measure of <RUS, we can use the fact that the sum of the measures of the angles around a point is 360 degrees.
We know that <PUQ = 82 degrees, <QUR = 24 degrees, and <SUT = 51 degrees.
Since these angles form a straight line (P-U-T), we can find the measure of <PUT by subtracting the sum of the given angles from 360 degrees:
<PUT = 360 degrees - (<PUQ + <QUR + <SUT)
= 360 degrees - (82 degrees + 24 degrees + 51 degrees)
= 360 degrees - 157 degrees
= 203 degrees
Now, we can find the measure of <RUS by subtracting <PUT from 180 degrees (since <PUT and <RUS are adjacent angles on a straight line):
<RUS = 180 degrees - <PUT
= 180 degrees - 203 degrees
= -23 degrees
Since angles cannot have negative measures, we conclude that the measure of <RUS is 23 degrees.
The correct answer is C) 23 degrees.