Quadrilateral jklm is a rhombus. the diagonals intersect at n. if the measure of angle kjl is 2x + 5° and angle mjn = 3x – 8 find the measure of angle klm.

The measure of angle KLM is 62°

Step-by-step explanation:

* Lets revise the properties of the rhombus

- The rhombus has 4 equal sides in length

- Every two opposite angles are equal in measure

- The two diagonals bisect each other

- The two diagonals perpendicular to each other

- The two diagonals bisect the vertices angles

* Lets solve the problem

∵ JKLM is a rhombus

∴ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus

∵ JL and KM are diagonals in the rhombus and intersect each

   other at N

∴ JL bisects ∠MJK

∴ m∠KJL = m∠MJN

∵ m∠KJL = (2x + 5)°

∵ m∠MJN = (3x - 8)°

∴ 2x + 5 = 3x - 8 ⇒ subtract 2x from both sides

∴ 5 = x - 8 ⇒ add 8 to both sides

∴ 13 = x

∴ The value of x = 13

∵ m∠KJL = (2x + 5)° ⇒ substitute the value of x

∴ m∠KJL = 2(13) + 5 = 26 + 5 = 31°

∵ m∠KJL = 1/2 m∠MJK

∴ m∠MJK = 2 m∠KJL

∴ m∠ MJK = 2 × 31° = 62°

∵ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus

∴ m∠KLM = 62°