The height RQ is drawn from the vertex R of the right angle of triangle SRT. Find the angle SRQ if the angle T is 32 degrees.

There are different ways to solve the problem, let’s consider them.
Option 1.
Find the second acute angle S in triangle SRT:
∠ S = 90 ° – ∠ T = 90 ° – 32 ° = 58 °.
In a right-angled triangle SQR we find an acute angle R, knowing the degree measure of the angle S:
∠ R = 90 ° – ∠ S = 90 ° – 58 ° = 32 °.
Option 2.
Find the second acute angle S in triangle SRT:
∠ S = 90 ° – ∠ T = 90 ° – 32 ° = 58 °.
The SRT triangle is similar to the SQR triangle (right-angled triangles, common acute angle S). Equality of angles follows from the similarity of triangles:
∠ STR = ∠ SRQ = 32 °.
Answer: The degree measure of the SRQ angle is 32 °.