The outer angle of a triangle is 3 times one of its non-adjacent angles, and the other non-adjacent

The outer angle of a triangle is 3 times one of its non-adjacent angles, and the other non-adjacent angle is 76 °. Find an adjacent corner.

Let the first angle of the triangle be x degrees, the second angle is 76 °, and the outside angle not adjacent to the first two inside corners is 3x degrees. The third corner of the triangle adjacent to the outer corner is (180 – 3x) degrees (since the sum of the outer and inner angles at one vertex of the triangle is 180 °). The angles of a triangle add up to 180 ° or (x + (180 – 3x) + 76) degrees. Let’s make an equation and solve it.

x + (180 – 3x) + 76 = 180;

x + 180 – 3x + 76 = 180;

-4x = 180 – 180 – 76;

-4x = -76;

x = -76: (-4);

x = 38 ° – first angle;

180 – 3x = 180 – 38 * 3 = 180 – 114 = 66 ° – the third angle.

Answer. 66 °