# One of the outer corners of a triangle is 98 degrees. Find the angles of a triangle

**One of the outer corners of a triangle is 98 degrees. Find the angles of a triangle that are not adjacent to it if one of these angles is 6 times smaller than the other.**

The outer and inner angles of a triangle at one vertex are adjacent angles and of the sum is 180 degrees. Find the inner corner of the triangle adjacent to the outer corner of 98 °.

180 ° – 98 ° = 82 °

Find the other two corners of the triangle.

Let the first angle of the triangle be x degrees, then the second angle of the triangle is 6x degrees, and the third angle of the triangle is 82 degrees. According to the theorem on the sum of the angles of a triangle (The sum of the angles of a triangle is 180 °), the sum of the angles is (x + 6x + 82) degrees or 180 °. Let’s make an equation and solve it.

x + 6x + 82 = 180;

7x + 82 = 180;

7x = 180 – 82;

7x = 98;

x = 98: 7;

x = 14 °;

6x = 14 * 6 = 84 °.

Answer. 14 °, 84 °.