Question

Find (m∠ RSU) if (m∠ UST = 50) and (m∠ RST = 72).
a) 58
b) 62
c) 78
d) 122

Answer 1

To find the measure of angle RSU, we subtract the measures of angles UST and RST from 180. The measure of angle RSU is 122 degrees.

Step-by-step explanation:

To find the measure of angle RSU, we need to use the angle sum property of triangles. In triangle UST, the sum of angles UST, STU, and UTS is 180 degrees. Since we know that angle UST is 50 degrees and angle RST is 72 degrees, we can subtract their measures from 180 to find the measure of angle TSU: 180 - 50 - 72 = 58 degrees.

Now, we can use the angle sum property of triangle RSU to find the measure of angle RSU. The sum of angles RSU, SUR, and USR is 180 degrees. Since we know that angle TSU is 58 degrees, we can subtract its measure from 180 to find the measure of angle RSU: 180 - 58 = 122 degrees.

Therefore, the measure of angle RSU is 122 degrees, which corresponds to option (d) in the given choices.