Determine the triangles in which the angle at the vertex B is equal to 30 °.

Given:
triangle ABC;
angle B = 30 °.
Identify possible triangles.
Solution:
1) The sum of the degree measures of the angles of any triangle is 180 degrees, then
angle A + angle C = 180 ° – 30 °;
angle A + angle C = = 150 °;
2) If angle B = 30 °, angle A = 90 ° and angle C = 60 ° then triangle ABC is rectangular;
3) If angle B = 30 °, angle A = 100 ° and angle C = 50 ° then triangle ABC is obtuse;
4) If angle B = 30 °, angle A = 75 ° and angle C = 75 °, then triangle ABC is acute-angled and isosceles.