Question

Prove that “ the sum of the three angles of a triangle is 180"​

Answer 1

To Prove :

• “ the sum of the three angles of a triangle is 180"

Solution :

l || BC & AB is traversal

∠2 + ∠4 ( Alternate interior angle)

l || BC & AC is a traversal

∠5 + ∠3 ( Alternate interior angle)

∠1 + ∠4 + ∠5 = 180° ( supplementary angle)

∠1 + ∠2 + ∠3 = 180°

hence proved

Extra information :

• Volume of cylinder = πr²h
• T.S.A of cylinder = 2πrh + 2πr²
• Volume of cone = ⅓ πr²h
• C.S.A of cone = πrl
• T.S.A of cone = πrl + πr²
• Volume of cuboid = l × b × h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)

Answer 2

Step-by-step explanation:

Given :

• ABC is a triangle the sum of the three angles of a triangle is 180"

To prove :

• Prove that “ the sum of the three angles of a triangle is 180"

Construction :

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

Proof :

∵ EF || AB

$\sf alternate\: interior \:angles \:$

$\sf x = \angle\ B \\ \\ \sf y = \angle \: A$

Now ,

x + ∠C + y = 180°

→ Substituting value of x and y

∠B + ∠C + ∠A = 180°

∴ ∠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 .