Question

an exterior angle of triange is 80 and two opposite interior angle are equal then find the each angel

Answer 1

100 and another will be 40 by linear pair and angle sum property

Answer 2

There are three relevant theorems to help us here:

The angle sum theorem: a + b + c = 180° (interior angles of a triangle sum to 180°)

The linear pair theorem: b + d = 180° (linear pairs are supplementary)

And by combining the two, and a little Algebra, you get

Exterior angle theorem: a + c = d (The exterior angle is equal to the sum of the two remote interior angles)

In the problem, you were given an exterior angle, d = 120°, and a remote interior angle (a or c, they’re interchangeable).

We know from linear pair theorem that b