Question

In ARST, mZR = (x + 17)°, mZS = (2x − 2)°, and mZT = (5x + 5)°. FindmZS.

Answer 1

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

`m\angle R+m\angle S+m\angle T=180\degree`

Let us substitute the given values and solve for x.

`\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=(160)/(8) \\ x=20 \end{gathered}`

So, the value of x is 20

Now we can find the measure of angle m∠S

`\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}`

Therefore, the measure of angle m∠S is 38°