In a right-angled triangle, two acute angles are equal. What is the smallest outer angle at the apex of this triangle?

1. Considering that, according to the problem statement, the acute angles of the rectangle are equal, we calculate the value of each of them:

(180 ° – 90 °) / 2 = 45 °.

2. We calculate the value of the outer angles adjacent to the inner angles of the triangle, equal to 45 °:

180 ° – 45 ° = 135 °.

3. We calculate the value of the external angle adjacent to the internal angle of the triangle, equal to 90 °:

180 ° – 90 ° = 90 °.

Answer: The smallest outer angle at the vertices of a triangle is 90 °.