Question

The measures of the angles of Angle RST are given by these expressions. Angle R is 31 and Angle S is (x + 4) and Angle T is (3x + 9). Find the value of x and then find the Angle of S and T

Answer 1

Using the triangle sum theorem, which states the sum of the three interior angles in a triangle is always 180. Therefore:

$\begin{gathered} m\angle R+m\angle S+m\angle T=180 \\ 31+x+4+3x+9=180 \\ add_{\text{ }}like_{\text{ }}terms \\ 44+4x=180 \\ Solve_{\text{ }}for_{\text{ }}x \\ 4x=180-44 \\ 4x=136 \\ x=\frac{136}{4} \\ x=34 \end{gathered}$

Now that we know the value of x, we will be able to know the value of S and T, so:

$\begin{gathered} m\angle S=x+4=34+4=38 \\ m\angle T=3x+9=3(34)+9=111 \end{gathered}$