Question

prove that sum of three angles in a triangle is 180 degree​

Answer 1

Given :

• ABC is a triangle

To prove :

• Sum of all the angles is 180° ,i.e. ∠A+ ∠B + ∠C = 180°

Construction :

• Construct a line EF touching the vertex C of ∆ABC such that EF// AB .

Proof :

$\because$ EF // AB

$\tt alternate\: interior \:angles \begin{cases} \tt x = \angle\ B \\ \\ \tt y = \angle \: A \end{cases}$

Now , since EF is a straight line ,

x + ∠C + y= 180°

→Substituting value of x and y

∠B+ ∠C + ∠A = 180°

$\therefore$ ∠A + ∠B + ∠C = 180°

Hence , the sum of all interior angles of a triangle is 180° regardless of the type of triangle .

This is also called angle sum property of a triangle .