One of the inner angles of a triangle is 24 larger than the other, and the outer angle

One of the inner angles of a triangle is 24 larger than the other, and the outer angle at the apex of the third is 106. Find the angles of a triangle

It is known from the condition that one of the inner angles of the triangle is 24 ° larger than the other. Let’s denote by x ° the smaller angle of the triangle, then the larger angle will be denoted by (x + 24) °. We also know that the outer angle at the top of the third is 106 °.

Let’s calculate the third angle of the triangle. The sum of the outer and inner angles at one of the vertices of the triangle is 180 °.

Looking for the third corner:

180 – 106 = 74 °.

The angles of a triangle add up to 180 °.

x + (x + 24) + 74 = 180;

2x = 180 – 74 – 24;

2x = 82;

x = 41 ° smaller angle and 41 + 24 = 65 ° another angle.

Answer: 41 °; 65 °; 74 °.