▢MRPN is cyclic, ∠ R = (5x – 13)°, ∠ N = (4x + 4)°. Find measures of ∠ R and ∠ N.

Explanation:- 

Using the fact that opposite angles of a cyclic quadrilateral are supplementary, we have:

∠R + ∠N = 180°

Substituting the given values, we get:

5x – 13° + 4x + 4° = 180°

Combining like terms and simplifying, we get:

9x – 9° = 180°

Adding 9° to both sides, we get:

9x = 189°

Dividing by 9, we get:

x = 21°

Substituting this value for x, we can find the measures of angles R and N:

∠R = 5x – 13° = 5(21°) – 13° = 105° – 13° = 92°

∠N = 4x + 4° = 4(21°) + 4° = 84° + 4° = 88°

Therefore, the measures of angles R and N are 92° and 88°, respectively.