Question

given rhombus fghi below. if m∠hij = 52°, find m∠fij. answer attempt 3 out of 3 m∠fij = | ° submit answer

Explanation:

Step1: Recall rhombus diagonal properties

In a rhombus, diagonals are perpendicular bisectors and bisect the angles. Also, adjacent angles in a rhombus are supplementary, but here we use the right triangle formed. Since \( \angle HIJ = 52^\circ \) and \( \angle FIJ \) is complementary to \( \angle HIJ \) (because diagonals of a rhombus are perpendicular, so \( \angle HIJ + \angle FIJ = 90^\circ \)).

Step2: Calculate \( m\angle FIJ \)

Using the complementary angles formula: \( m\angle FIJ = 90^\circ - m\angle HIJ \). Substitute \( m\angle HIJ = 52^\circ \), we get \( m\angle FIJ = 90^\circ - 52^\circ = 38^\circ \).

Answer:

\( 38^\circ \)