Find the angle B of triangle ABE if it is 30 degrees less than E, and A = 80.

In any form of triangles, the sum of all angles is 180º:

∠А + ∠В + ∠С = 180º.

Since the degree measure of the angle ∠A is equal to 80º, and ∠B is 30º less than the value of the angle ∠С, then we express:

x is the degree measure of the angle ∠В;

x + 30 – degree measure of the angle ∠E;

x + x + 30 + 80 = 180;

x + x = 180 – 80 – 30;

2x = 70;

x = 70/2 = 35;

∠В = 35º;

∠E = 35º + 30º = 65º.

Answer: the degree measure of the angle ∠B is equal to 35º.