Question

Angle RST measures 15x - 14 degrees and has ray SU in its interior. If angle RSU is 3x - 12 and angle UST is 58 degrees, the measure of angle RST is ___ degrees.

a)130
b) 128
c) 126
d) 124

Answer 1

To find the measure of angle RST, set up an equation using the given information and solve for x. Substitute x back into the expression for angle RST to find the measure.

Step-by-step explanation:

To find the measure of angle RST, we need to set up an equation using the given information. We know that angle RSU is 3x - 12 degrees, angle UST is 58 degrees, and angle RST is 15x - 14 degrees.

Based on the picture formed by the angles, we can set up the equation: 3x - 12 + 58 + 15x - 14 = 180.

Simplifying the equation, we get: 18x + 32 = 180. Solving for x, we find x = 8.

Substituting x back into the expression for angle RST, we get 15x - 14 = 15(8) - 14 = 118 degrees.

Therefore, the measure of angle RST is 118 degrees.