What would be a situation in which the lengths of two sides of a right triangle are known, but the measure of an angle is needed.

Never.  If you know two sides of a right triangle you can always find the third using the pythagorean theorem.

 Once all sides are known, you can find the three angles: one is surely right, since you have a right triangle. The other two can be found using the sine law.

Step-by-step explanation:

correct on EDGE2022

y=x+9

?

step-by-step explanation:

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°