Question

The exterior angles obtained on producing the base of a triangleABC both ways are 100degree and 120degree. Find all the angles of the triangle.

Answer 1

Let ABC be the triangle with BC produced on both sides B and C till E and F respectively.

Angle ABE = 100 degrees

Angle ACF = 120 degrees

angle ABE + angle ABC = 180 degrees

=> 100 degrees+angle ABC=180degrees

=> angle ABC = (180-100) degrees

=> angle ABC = 80 degrees

angle ACF + angle ACB = 180 degrees

=> 120 degrees+angle ACB=180 degrees

=> angle ACB = (180-120) degrees

=> angle ACB = 60 degrees

angle BAC = (180-80-60) degrees

= (180-140) degrees

= 40 degrees

So, the three angles are 80,60,40 degrees.