Question

the exterior angle of a triangle is 130 and the two interior opposite angles are in the ratio of 6:7 find the angles of the triangle​

Answer 1

60°,70°and 50°

Step-by-step explanation:

dum of interior angle is equal to exterior angle

let 6:7 equal to 6x/7x

so 6x+7x= 130°

so x=10 and 6x=60° , 7x=70°

and sum of all angles is 180°

so 60°+70°+y=180°

so y=50°

Answer 2

AnsWer :

• The exterior angle of a triangle is 130°
• The two interior opposite angles are in the ratio of 6:7.

We have to find the measure of each angle of traingle.

★ According to the Question now :

Let the two interior opposite angles be as 6x and 7x.

⇒ Exterior angle of ∆ = Sum of interior opposite angles

⇒ 130° = 6x + 7x

⇒ 130° = 13x

⇒ x = 130 ÷ 13

⇒ x = 10°

Hence,the two opposite interior angles are :

⇒ First opposite interior angle = 6x

⇒ First opposite interior angle = 6 × 10

⇒ First opposite interior angle = 60°

⇒ Second opposite interior angle = 7x

⇒ Second opposite interior angle = 7 × 10

⇒ Second opposite interior angle = 70°

Now,let's find the measure of third angle of ∆ :

• Let third angle of ∆ be n.

⇒ 60° + 70° + n = 180° {Angle sum property of ∆}

⇒ 130° + n = 180°

⇒ n = 180° - 130°

⇒ n = 50°

• Hence,the measure of third angle is 50°.