Question

Why Is Triangle Always $180°$?

Answer 1

Angle sum property of a triangle:

• The sum of interior angles of a triangle is $180°$.
• One exterior angle of a triangle is equal to the sum of the other two angles in the triangle.
• The exterior angle is obtained by extending the side of the triangle. Since it is a straight line, the angle is $180°$.

• Here, $\angle BCD=180°\left(\because \mathrm{linear}\mathrm{pair}\right)$ and $\angle ACD=\angle BAC+\angle ABC$.
• The formula to find the sum of interior angles of a regular polygon is $\left(n-2\right)\times 180°$, where $n$is the number of sides of the polygon.

Hence, the Triangle Always $180°$