Find the unknown angles of a triangle if one of them is 31 degrees and one of the outside angles is 132 degrees.

1. Vertices of the triangle A, B, C. ∠O = 132 ° – the outer corner of the triangle at the vertex B.

∠А = 31 °.

2. The external angle of the triangle ∠O, according to its properties, is equal to the total value of two internal angles that are not adjacent to it:

∠О = ∠А + ∠С = 132 °.

31 ° + ∠С ° = 132 °.

∠С = 132 ° – 31 ° = 101 °.

2. Considering that the total value of all internal angles of the triangle is 180 °, we calculate the value of ∠В:

∠В = 180 ° – ∠А – ∠С = 180 ° – 31 ° – 101 ° = 48 °.

Answer: ∠В = 48 °, ∠С = 101 °.



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