In a triangle ABC, the angle a is 76º. The outside angle at the vertices is 94º. Find the angle c.

In triangle ABC it is known:

Angle A = 76 °;
Outside angle at apex В = 94 °;
Find corner C.

Solution:

1) If the outside angle B is 94 °, then the inside angle B is:

180 ° – 94 ° = 100 ° + 80 ° – 90 ° – 4 ° = 10 ° + 80 ° – 4 ° = 80 ° + 6 ° = 86 °.

2) If you know 2 angles in the triangle 76 ° and 86 °, then we find the third angle of the triangle ABC.

Angle С = 180 ° – 76 ° – 86 ° = 180 ° – 70 ° – 6 ° – 80 ° – 6 ° = 110 ° – 6 ° – 80 ° – 6 ° = 30 ° – 6 ° – 6 ° = 30 ° – 12 ° = 30 ° – 10 ° – 2 ° = 20 ° – 2 ° = 18 °;

Answer: Angle C = 18 °.