Question

An exterior angle of a triangle is 100° and its interior opposite angles are equal to each other. Find the measure of each angle of the triangle.

Answer 1

Suppose the interior opposite angles of an exterior angle 100^o are x^o and x^o.
We know that the exterior angle of a triangle is equal to the sum of the interior opposite angles.

∴ x + x = 100
2x= 100
x= 50

Also, sum of the angles of any triangle is 180°.
Let the measure of the third angle be y°.

∴ x + x + y = 180
50 + 50 + y= 180
y = 80

Hence, the angles are of the measures 50°, 50° and 80°.