Answer:
x=3
Step-by-step explanation:
Hi there!
We are given ΔRTS, m<T=25x, m<S=57+x (both inside triangle RTS), and m<TRQ (outside of ΔRTS)=45x
We want to solve for x.
We can use the exterior angle theorem, which states that a measure of an exterior angle (an angle outside of a triangle) is equal to the sum of two remote interior angles (adding the values of two different angles that are inside the triangle gives us the value of the angle outside of a triangle).
Based on the theorem, this is true:
m<T+ m<S= m<RTQ
We can plug in values we know into the equation to get:
25x+57+x=45x
Now combine like terms
26x+57=45x
Subtract 26 from both sides
57=19x
Divide both sides by 19
3=x
Hope this helps!
