A side of the triangle below has been extended to form an exterior angle of 133°. Find the value of x.

Answer 1

We can see that the exterior angle $133^\circ$ is equal to the sum of the two remote interior angles of the triangle, which are $x$ and $x+5^\circ$. So we have $$x + (x+5^\circ) = 133^\circ.$$ Simplifying the left side gives $2x+5^\circ=133^\circ$, so $2x = 128^\circ$ and $x=\boxed{64^\circ}$.