The outer angle of a right-angled triangle at apex B is 120 degrees. Angle C = 90 degrees.

The outer angle of a right-angled triangle at apex B is 120 degrees. Angle C = 90 degrees. Find the sharp corners in the triangle.

From the condition it is known that the outer angle of a right-angled triangle at the apex is 120 °, and the angle C is 90 °.

In order to find the acute angles of a triangle, let’s recall the property of the external angle, it says that the external angle of a triangle is equal to the sum of two angles of the triangle that are not adjacent to it.

We introduce the variable x, denoting it one of the acute angles of the triangle.

So the sum of the angles, 90 ° and an acute, not adjacent to the outer angle of 120 °, is equal to 120 °.

Let’s compose and solve the equation.

x + 90 = 120;

x = 120 – 90;

x = 30 °;

The third inner corner is 180 ° – (90 ° + 30 °) = 60 °.