TopTriangle Sum Theorem states that sum of all angles of a triangle is equals to 180 degrees.

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.

To prove:

∠ ACD = ∠ A +∠ B,

Proof:

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.

STEP 2:

∠ 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).