solve for the value of r.

Explanation:

Step1: Recall angle - sum property

The sum of the two non - overlapping angles is 90° (since the right - angle is 90°). So, 52+(4r - 6)=90.

Step2: Simplify the left - hand side

First, combine like terms: 52-6 + 4r=90, which gives 46+4r=90.

Step3: Isolate the variable term

Subtract 46 from both sides: 4r=90 - 46. So, 4r=44.

Step4: Solve for r

Divide both sides by 4: r = $\frac{44}{4}$ = 11.

Answer:

11