MK = 24, JL = 20, and m The quadrilateral below is a rhombus. Find the missing measures. Any decimal answers should be rounded to the nearest tenth.

NK =

m

NL =

m

ML =

m

JM =

m

m

The answer is below

Step-by-step explanation:

If the quadrilateral below is a rhombus, find the missing measures.

MK = 24, JL = 20, and mZMJL = 50°

Solution:

A rhombus is a quadrilateral (has four sides and four angles) such that all the sides are of equal length.

The diagonals of a rhombus bisect each other.

NK = MK / 2 (diagonals of a rhombus bisect each other)

NK = 24 / 2 = 12

NL = JL / 2 (diagonals of a rhombus bisect each other)

NL = 20 / 2 = 10

In triangle MNL, ∠N = 90°

MN = NK = 12 , NL = 10. Using Pythagorean theorem:

ML² = MN² + NL²

ML² = 12² + 10²

ML² = 244

ML = √244

ML = 2√61 = 15.62

JM = ML  = 15.62 (all sides of a rhombus are equal)

∠KNL = 90° (diagonals are perpendicular bisectors)

∠KJL = ∠MJL (diagonals bisect angles)

∠KJL = 50°

∠MJK = ∠KJL + ∠MJL = 50 + 50 = 100°

∠MJK = ∠MLK (opposite angles are equal)

∠MLK = 100°

∠NJK + ∠JNK + ∠JKM = 180° (sum of angles in triangle)

50 + 90 + ∠JKM = 180

∠JKM = 40°

∠JKL = 2 * ∠JKM (diagonal bisect angle)

∠JKL = 2 * 40

∠JKL = 80°

∠JKL = ∠JML (opposite angles are equal)

∠JML = 80°