Question

Prove that the sum of angles of a triangle is $180°$.

Answer 1

STEP 1 : Assumption

Consider a triangle $ABC$ as shown in figure and through $A$, draw a line $l$ parallel to $BC$.

Mark the angles $\angle 1,\angle 2,\angle 3,\angle 4$ and $\angle 5$ as shown in the figure.

STEP 2 : Proving that sum of the angles of a triangle is $\mathbf{180}\mathbf{°}$

Since, line $l$ parallel to $BC$ therefore,

$\angle 2=\angle 4$ (Alternate interior angles) $...\left(1\right)$

$\angle 3=\angle 5$ (Alternate interior angles) $...\left(2\right)$

Adding equation $\left(1\right)$ and

We know that angles on a straight line add up to $180°$

$\therefore \angle 1+\angle 4+\angle 5=180°$

$\Rightarrow \angle 1+\angle 2+\angle 3=180°$

Hence proved that the sum of angles of a triangle is $180°$.