Question

An exterior angle of a triangle is 110. And it's interior opposite angles are in ratio 3.8 find its all interior angles

Answer 1

Calculation of interior angles of triangle

Answer: three interior angles of the triangle are 30 degree , 80 degree and 70 degree.

Explanation:

given that exterior angle of triangle = 110

lets assume three angles of triangle be ∠ 1 , ∠2 and ∠3

let ∠ 1 , ∠2 be interior opposite angle to exterior angle of 110 degree.

As interior opposite angles are in ratio 3 : 8 ,

lets assume ∠ 1  = 3y and  ∠2 = 8y.

Now we will be using following theorem to calculate two interior opposite angles

Theorem says "Sum of interior opposite angles of traingle is equal to an exterior angle"

=> ∠ 1  +  ∠2 = exterior angle

=> 3y + 8y = 110

=> 11y = 110

=> y = 110/11 = 10

∠ 1 = 3y = 3 x 10 = 30

∠2 = 8y = 8 x 10 = 80

using angle sum property of traingle we can say that

∠ 1 + ∠2 + ∠3 = 180

=> 30 + 80 + ∠3  = 180

=> ∠3  = 180 - 110 = 70

hence three interior angles of the traingle are 30 degree , 80 degree and 70 degree.

#answerwithquality

#BAL

Answer 2

Exterior angle is sum of opposite interior angles

Let the angles be 3x,8x

So 3x+8x= 110

11x=110

x= 110/11

x= 10

So angle 3x = 30

8x = 80

And third angle is 180-(30+80)

= 180-110 = 70

Hope this helps!!!!