We have a triangle △RST where the measure of angles are given as
m∠R = x + 17
m∠S = 2x - 2
m∠T = 5x + 5
We know that the sum of all three angles in a triangle must be equal to 180°
So, we can write the following equation
[tex]m\angle R+m\angle S+m\angle T=180\degree[/tex]
Let us substitute the given values and solve for x.
[tex]\begin{gathered} (x+17)+(2x-2)+(5x+5)=180 \\ (x+2x+5x)+(17-2+5)=180 \\ 8x+20=180 \\ 8x=180-20 \\ 8x=160 \\ x=\frac{160}{8} \\ x=20 \end{gathered}[/tex]
So, the value of x is 20
Now we can find the measure of angle m∠S
[tex]\begin{gathered} m\angle S=2x-2 \\ m\angle S=2(20)-2 \\ m\angle S=40-2 \\ m\angle S=38\degree \end{gathered}[/tex]
Therefore, the measure of angle m∠S is 38°
