Are two right triangles similar if one has an angle of 40 degrees and the other has an angle of 50 degrees?

Similar triangles are triangles in which the angles are respectively equal, and the sides of one are respectively proportional to the sides of the other triangle.

In order to determine whether these triangles are similar, you need to calculate the degree measures of all the angles of these triangles.

Since the sum of all the angles of the triangle is 180º, and one of the angles (∠С) is a straight line, then:

∠А = 180º – ∠С – ∠В;

∠А = 180º – 90º – 40º = 50º;

∠В1 = 180º – ∠С1 –∠А1;

∠В1 = 180º – 90º – 50º = 40º.

∠А = ∠А1;

∠В = ∠В1;

∠С = ∠С1.

Answer: since in the triangles ΔАВС and ΔА1В1С1 the corresponding angles are equal, then these triangles are similar.