Question

one of the exterior Angles of a triangle is 125°and the interior opposite angles are in the ratio 2:3 please find the Angles of the triangle ​

Answer 1

Hey there!

Given , one exterior angle is 125°

Interior angles are in ration 2:3

Let the angles be 2x and 3x

Now , 125° = 2x + 3x

=> 5x = 125°

=> x = 125/5

=> x = 25°

Now the angles are ,

2x = 2(25)=50° &
3x = 3(25) = 75°

Hope this helps you :)
Have a good day :)

Answer 2

Angles of the triangles are 55° , 50° , 75°

Explanation:

Exterior angle property of triangle:

The exterior angle of a triangle equals the sum of opposite interior angles.

Ratio of interior opposite angle = 2 : 3

Interior opposite angles are 2x , 3x

2x + 3x = 125

5x = 125

x = 125/5

`\boxed{x = 25}`

2x = 2*25 = 50°

3x = 3*25 = 75°

Let the third angle of the triangle = y

Sum of all angles of triangle = 180

50 + 75 + y = 180

125 + y = 180

y = 180 - 125

y = 55°

Angles of the triangles are 55° , 50° , 75°