In a right-angled triangle, one of the acute angles is 52 °. Determine the size of the third angle.

According to the conditions of this task, it is required to determine one unknown angle of a right-angled triangle if another acute angle of a right-angled triangle is known. We will calculate the unknown angle based on two positions:

1) In a right-angled triangle, one angle is 90 °.

2) The sum of all the angles of any triangle is 180 °.

Thus, we will write an expression and calculate the unknown acute angle of a right-angled triangle:

180 ° – 90 ° – 52 ° = 90 ° – 52 ° = 38 °

Answer: The third angle is 38 °.