Question

Prove the exterior angles theorem:
Given: triangle ABC w/ exterior angle ACD
Prove: measure of angle ACD= measure of angle A +measure of angle B.

Please help! i dont know how to do this proof!

Answer 1

if the sum of the angles is 180, then A + B + C = 180. Solving for C, you get C=180-A-B.
For the exterior angle, angle DCA is supplementary to angle ACB. So, DCA + ACB = 180. SInce you know angle ACB (simplified to angle C in the first line), you can substitute that
DCA+180-A-B=180. IF you simplify this, you get DCA=A+B