Question

one of the exterior angle of a triangle is 105 and the interior opposite angle are in the ratio 2:5 . find the angles of the triangle ​

Answer 1

Answer:

2x+5x=105o

7x=105o ⟹x=15o

Therefore the interior opposite angles to the angle 105o are 2x=2(15)=30o and 5x=5(15)=75o

Let the third angle of the triangle be C

We have the sum of interior angles of a triangle is 180o

∴30o+75o+C=180o

C=180o−75o−30o=180o−105o

C=75o

Hence, the angles are 30o,75o,75o.