Question

Geometry, How do I do this? I tried and I keep getting confused

Answer 1

Given triangle RST is am isosceles triangle.

Therefore,

$\angle R=\angle T$

So,

$\begin{gathered} 15x-31=9x+11 \\ 15x-9x=11+31 \\ 6x=42 \\ x=\frac{42}{6} \\ x=7 \end{gathered}$

Hence,

$\begin{gathered} \angle R=15\times7-31 \\ =74 \\ \angle T=9\times7+11 \\ =74 \end{gathered}$

Since the sum of interior angles of a triangle is 180,

$\begin{gathered} \angle S+\angle R+\angle T=180 \\ \angle S+74+74=180 \\ \angle s=180-148 \\ \angle S=32 \end{gathered}$

Therefore angle S is 32 degree.