Answer:
The answer is below
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°