Question

Prove that sum of angles of triangle is $180$ degree.

Answer 1

To prove:

The sum of angles of triangle is $180$ degree.

Proof:

Lets take a triangle $△ABC$

Consider base $BC$, draw a line $MN$, parallel to $BC$

Now, $AB$ & $AC$ will out as transversals.
In figure,
$AB$ is transversal, and $MN\parallel BC$
$\Rightarrow \angle 2=\angle 4$ [Since, alternate interior angles]--(1)
$AC$ is transversal, and $MN\parallel BC$
$\Rightarrow \angle 3=\angle 5$ [Since, alternate interior angles]--(2)

Adding equation(i) and (ii), we get
$\angle 2+\angle 3=\angle 4+\angle 5$
Adding $\angle 1$ on both sides, we get
$\Rightarrow \angle 1+\angle 2+\angle 3=\angle 1+\angle 4+\angle 5$.....(iii)
Since, $\angle 4+\angle 1+\angle 5$ will form a linear pair.
As we know that the some of angles of a linear pair is ${180}^{\circ }$
$\Rightarrow \angle 4+\angle 1+\angle 5={180}^{\circ }$
Substitute above equation in equation(iii), we get
$\Rightarrow \angle 2+\angle 1+\angle 3={180}^{\circ }$

i.e., in $△ABC$, $\angle A+\angle B+\angle C={180}^{\circ }$

Hence, proved.