The interior angles of a triangle all add up to 180°. In fact, for any n-sided polygon, the sum of the measures of the interior angles is 180°(n–2).
So, these three angles must add up to 180°.
That means, m∠A + m∠B + m∠C = 180°.
Substituting our known values, we write [tex]35 + 52 + 3(x+2)=180[/tex].
We then simplify this expression to solve for x. (Alternately, you could solve for m∠C first, but it's clearer to first solve for x.)
[tex]3x+6=93 \\ x=29[/tex]
Then, to find m∠C, substitute 29° for x in [tex]3(x+2)[/tex] to get 93°.
(a) 29
(b) 93°
