Question

If the exterior angle of a triangle is 140° and its interior opposite angles are equal, find all the interior angles of the triangle.

Answer 1

Given the exterior angle = 140° 

Interior opposite angle are equal.

Let one of the interior opposite angle be x. 

Then x + x = 140°. 

[∵ Exterior angle = sum of interior opposite angles] 

2x = 140° 

x = \(\frac{140°}{2}\)

= 70° 

x = 70° 

Interior opposite angle = 70°, 70°. 

Sum of the three angles of a triangle = 180°. 

70° + 70° + Third angle = 180°

140° + Third angle = 180° 

Third angle = 180° – 140° 

= 40° 

∴ Interior angle are 40°, 70°, 70°.