If A, B, C are angles of a triangle then sum of these three angles of triangle will be equals to 180 degree.
So we can say that:
A + B + C =180.
Corollary of Triangle Sum Theorem states that if one side of a triangle is extended, then exterior angle so formed is equals to the sum of interior opposite angles.
Suppose in triangle ABC, BC is extended to D and we have to prove that angle ACD = angle A + angle B. Now we will prove corollary triangle sum theorem.
∠ ACD = ∠ A +∠ B,
STEP 1: We can write
∠ ACB + ∠ ACD = 180 degrees ----- equation 1
Reason behind this is that angle ACB and angle ACD form a linear pair and we know that sum of angles in linear pair is 180 degree.
So we can write sum of these two angles equals to 180 degree.
∠ A + ∠ B + ∠ ACB = 180 degrees ------equation 2
According to Triangles sum theorem “sum of the angles of a triangle is 180 degrees”.
STEP 3: Now we can see that value of equation 1 and equation 2 is equal,
so we can write-
∠ ACD = ∠ A + ∠ B + ∠ ACB+ ∠ ACD = ∠ A + ∠ B + ∠ ACB,
∠ ACD = ∠ A + ∠ B + ∠ ACB - ∠ ACB,
∠ ACD = ∠ A + ∠ B (Hence proved).