find the midpoint of the angles

Question

angle ACB is obtuse. D lies on the interior of angle ACB. angle ACE is straight. angle ACD and angle FCE are vertical. CB bisects angle ECD. m angle DCB = 55°. Find m angle ACD and m angle ACF. For full credit, sketch a diagram that includes all given information and show ALL work.

Answer 1

If CB is the angle bisector, then m∠BCE is also 55° and since ∠ACE is straight, and straight angles are 180°, you can calculate m∠ACD by subtracting (180 - 55 - 55)

Now you know the m∠ACD and since ∠ACD and ∠FCE are vertical angles, they are congruent so you know the m∠FCE. Now you can calculate m∠ACF by subtracting (180 - m∠FCE)