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 = `(140^circ)/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°.