The outer angle of the triangle is 134 ° and the inner angle not adjacent to it is -47 °

The outer angle of the triangle is 134 ° and the inner angle not adjacent to it is -47 ° Find the unknown angles of the triangle

It is known:

Triangle ABC.

The outer corner of the triangle is the angle BAD = 134 °;

Angle B = 47 °.

Let’s find the unknown angles of the triangle ABC, that is, angle A and angle C.

1) Find the angle A, that is, the inner angle of the triangle, if its adjacent outer angle is known.

Angle A = 180 ° – angle BAD = 180 ° – 134 ° = 180 ° – 130 ° – 4 ° = 50 ° – 4 ° = 46 °;

2) In the triangle ABC 2 angles are known, then we find the third angle, that is, the angle C.

Angle C = 180 ° – 46 ° – 47 ° = 180 ° – 40 ° – 6 ° – 40 ° – 7 ° = 100 ° – 6 ° – 7 ° = 100 ° – 13 ° = 87 °.

Answer: angle A = 46 ° and angle C = 87 °.