Question

Prove that the sum of all angles of a triangle is 180 . Also, find the angles of a triangle if they are in ratio 5:6:7.

Answer 1

let the angles is x

by angle sum property

5x+6x+7x = 180°
18x = 180°
x = 180°÷18
x = 10°

since x =10°

5x = 50°
6x = 60°
7x = 70°

when we add all the angles

50°+60°+70° = 180°

Hence proved!

Answer 2

Statement : The sum of the angles of a triangle is 180°.

To prove : sum of the angles of ΔABC is 180°

Construction : Draw a line $lm$ parallel to BC.

Proof :

Since $lm$ || BC, we have ;

∠2 = ∠y ..... (i) . [Alternate interior angles]

Similarly,

∠1 = ∠z ....... (ii) . [Alternate interior angles]

Also, sum of angles at a point a on line $lm$ is 180°.

∴ ∠2 + ∠x + ∠1 = 180°

⇒ ∠y + ∠x + ∠z = 180°

⇒ ∠x + ∠y + ∠z = 180°

⇒ ∠A + ∠B + ∠C = 180°

Therefore,

Sum of all angles of a Δ is 180°

_______________________

Question 2 :

Let the measure of angles be 5x, 6x and 7x respectively.

According to the question ;

5x + 6x + 7x = 180°

⇒ 18x = 180

⇒ x = 180 / 18

⇒ x = 10

Hence, the measure of the angles are ;

5x = 5 * 10 = 50°
6x = 6 * 10 = 60°
7x = 7 * 10 = 70°