The two angles of a triangle are 3: 4, and the outer angle, not adjacent to either, is 105 degrees.

The two angles of a triangle are 3: 4, and the outer angle, not adjacent to either, is 105 degrees. Determine the inner corners of the triangle.

The outer and inner corners of a triangle at one vertex are adjacent. The sum of adjacent angles is 180 °. Hence, the degree measure of the angle adjacent to the given external angle of 105 ° is 180 ° – 105 ° = 75 °.

The other two angles of the triangle are 3: 4, which means that one of these angles contains 3 parts, and the other 4 of the same parts of the angle.

Let the degree measure of one part of the angle be x degrees, then the degree measure of the first angle is 3x degrees, and the degree measure of the second angle is 4x degrees. The sum of the angles of a triangle is 180 ° or (3x + 4x + 75) degrees. Let’s make an equation and solve it.

3x + 4x + 75 = 180;

7x = 180 – 75;

7x = 105;

x = 105: 7;

x = 15 ° – one part;

3x = 15 ° * 3 = 45 ° – the first angle;

4x = 15 ° * 4 = 60 °.

Answer. 75 °; 45 °; 60 °.