Question

the figure shown includes the linear pair of ∠frk and ∠vrk, where ∠brk and ∠frn are right - angles and m∠brn = 53°. the measure of ∠frk is by the since ∠frk and ∠brn are = 37° = 53° = 127° congruent supplementary complementary linear pair postulate congruent supplements theorem congruent complements theorem

Explanation:

Step1: Recall angle - relationship of linear pair

Linear - pair angles are supplementary, meaning their sum is 180°. Given that $\angle BRN = 53^{\circ}$ and $\angle BRK$ and $\angle FRN$ are right - angles (90° each), and $\angle FRK$ and $\angle VRK$ form a linear pair. Also, since $\angle BRK = 90^{\circ}$ and $\angle BRN+\angle NRK=\angle BRK$, we know that $\angle NRK = 90^{\circ}-\angle BRN$.

Step2: Calculate $\angle FRK$

Since $\angle FRN = 90^{\circ}$ and $\angle NRK = 90^{\circ}-\angle BRN$, and $\angle FRK+\angle NRK=\angle FRN$. Substituting $\angle BRN = 53^{\circ}$, we get $\angle NRK=90 - 53=37^{\circ}$. Then $\angle FRK = 90^{\circ}-\angle NRK$. So $\angle FRK = 37^{\circ}$.

Answer:

$37^{\circ}$