# Prove that the sum of the measures of the interior angles of a triangle is 180º.

A triangle is a polygon with three sides, three angles, and three vertices.

## Answer: Hence, it is proved that the sum of the measures of the interior angles is 180º.

Let's prove.

**Explanation:**

Given: A triangle is a polygon with three angles.

To prove: The sum of the measures of the interior angles is 180º.

Proof: Consider △ABC,

Let the measures of the interior angles of △ABC be ∠1, ∠2, and ∠3.

Now take a straight line XY parallel to BC

Since alternate interior angles are equal,

∠XAB = ∠ABC and ∠YAC = ∠ACB .......... (1)

⇒ XAY = 180º

⇒ ∠XAB + ∠BAC + ∠ YAC = 180º

Using (1), we get

∠ABC + ∠BAC + ∠ACB

Hence, Proved