In a right-angled triangle, one of the outer angles is 105 degrees. find the smaller corner of the right-angled triangle.

1. Vertices of the triangle A, B, C. ∠C = 90 °.

2. Suppose the outside angle at the vertex A is 105 °.

3. The total value of the external and internal angles at the vertex A is equal to 180 °, since they are adjacent. Taking this into account, we calculate the degree measure of the internal ∠А:

∠А = 180 ° – 105 ° = 75 °.

4. Considering that the total value of all internal angles of the triangle is 180 ° (according to its properties), we calculate the degree measure ∠В:

∠В = 180 ° – (∠А + ∠С) = 180 ° – (75 ° + 90 °) = 15 °.

Answer: ∠В = 15 ° – the smaller inner angle of the given triangle.