Question

State true or false:

The sum of interior angles of a triangle is ${180}^{\circ }$.

• A. True
• B. False

Answer 1

The correct option is A True

Let $ABC$ be a triangle.

Through point $A$ draw the line $EF\parallel BC$.

$\Rightarrow$ $\angle ABC=\angle EAB$ ....[ Alternate interior angles]

$\Rightarrow$ $\angle BCA=\angle FAC$ ....[ Alternate interior angles]

$\Rightarrow$ $\angle EAB+\angle BAC+\angle FAC={180}^o$ ....[ Linear pairs].

By substituting $\angle EAB=\angle ABC$ and $\angle FAC=\angle BCA$.

$\Rightarrow$ $\angle ABC+\angle CAB+\angle ACB={180}^o$.

$\therefore$ The sum of all the three interior angles of a triangle is ${180}^o.$

Hence, the given statement is true and option $A$ is correct.