Establish Angle Facts Using Arguments Practice Test

Because triangle angles add to $360^\circ$, $m\angle A + m\angle B + m\angle ACB = 360^\circ$, so $m\angle ACD = m\angle A + m\angle B$.

An exterior angle is always equal to the interior angle next to it, so $m\angle ACD = m\angle ACB$.

Since $\angle ACD$ and $\angle ACB$ form a linear pair, $m\angle ACD + m\angle ACB = 180^\circ$. Also, in triangle $ABC$, $m\angle A + m\angle B + m\angle ACB = 180^\circ$. Subtract $m\angle ACB$ from both equations to get $m\angle ACD = m\angle A + m\angle B$.

All angles around point $C$ add to $360^\circ$, so $m\angle ACD = 360^\circ - m\angle ACB$.