Question

The sum of all the three angles in a triangle is:

• A. 120${}^o$
• B. 180${}^o$
• C. 160${}^o$
• D. 360${}^o$

Answer 1

The correct option is B 180${}^o$

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 angles in a triangle is ${180}^o.$

Hence, option $B$ is correct.