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: a. 37° b. 53° c. 127° d. congruent e. supplementary f. complementary by the since ∠frk and ∠brn are

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, i.e., their sum is 180°. Since ∠FRK and ∠VRK form a linear pair. Also, ∠BRK and ∠FRN are right - angles (90° each), and ∠BRN = 53°.

Step2: Use angle - relationship

We know that ∠FRK+∠VRK = 180°. And since ∠BRK = 90° and ∠BRN = 53°, and ∠FRK and ∠BRN are complementary (because ∠BRK = 90° and ∠FRN = 90°). The measure of ∠FRK=90° - ∠BRN.

Step3: Calculate the angle

Substitute the value of ∠BRN = 53° into the formula. ∠FRK=90°−53° = 37°.

Answer:

37°