Find angle B of triangle BCE if it is 30 degrees less than angle C, and the outside angle at the vertex E is 130 degrees.

In order to calculate the degree measures of the angles ∠В and ∠С of the triangle, we first calculate the value of the angle ∠Е.
Since the sum of the outer and inner angles of a triangle at one vertex is 180º, then:
∠Е = 180º – φ;
∠E = 180º – 130º = 50º.
Since the sum of all the angles of the triangle is 180º:
∠В + ∠С + ∠Е = 180º, and the angle ∠В is 30º less than the angle ∠С, then we express:
x is the angle ∠В;
x + 30 – angle ∠С;
x + x + 30 + 50 = 180;
x + x = 180 – 50 – 30;
2x = 100;
x = 100/2 = 50;
∠В = 50º;
∠С = 50º + 30º = 80º.
Answer: the degree measure of the angle ∠B is equal to 50º.