Final answer:
To find m∠GJI in rhombus GHIJ, one must recognize that the diagonals of a rhombus bisect opposite angles. Therefore, m∠GJI is double m∠GJP, which is 38°, leading to the answer of 76°.
Step-by-step explanation:
The question asks us to find the measure of an angle within a rhombus, named m∠GJI, given that the measure of an adjacent angle (m∠GJP) is 38°. In a rhombus, the diagonals bisect each pair of opposite angles. Therefore, if m∠GJP = 38°, the angle adjacent to it across diagonal IG (which is m∠GJI) would have to be twice that measure because it is the full angle formed by the diagonals bisecting each other.
This means m∠GJI equals 2 × 38° = 76°.
The answer (a) 76° is the correct choice.