Answer:
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°
