Easy Angles 2

Let the measure of $\angle{C}$ be $x$ . We know that the sum of a triangle's angles is $180^\circ$ . We also know that the first two angles sum up to $110^\circ$ . From this, the measure of $\angle{C}$ is $180^\circ-110^\circ=70^\circ$ . The complement of an angle is $90-z$ , where $z$ is the measure of the angle in degrees. Thus, the complement of $\angle{C}$ is $90^\circ-70^\circ=\boxed{20^\circ}$ .

\[\begin{align} \angle A + \angle B + \angle C &= 180^{\circ} \\ (30^{\circ}) + (80^{\circ}) + \angle C &= 180^{\circ} \\ \angle C &= 70^{\circ} \implies \color{Blue}{[90 - 70 = \boxed{20}]}

\end{align}\]

$\angle ACB=180-80-30=70$

The sum of complimentary angles is $90^\circ$ . So the complement of $\angle ACB$ is $90-70=$ $\boxed{20}$