In ΔJKL, \overline{JL} JL
is extended through point L to point M, \text{m}\angle LJK = (2x+2)^{\circ}m∠LJK=(2x+2)
∘
, \text{m}\angle KLM = (8x-16)^{\circ}m∠KLM=(8x−16)
∘
, and \text{m}\angle JKL = (3x+6)^{\circ}m∠JKL=(3x+6)
∘
. Find \text{m}\angle KLM. m∠KLM.

9514 1404 393

  48°

Step-by-step explanation:

Exterior angle KLM is equal to the sum of the remote interior angles.

  ∠KLM = ∠LJK + ∠JKL

  (8x -16)° = (2x +2)° +(3x +6)°

  8x -16 = 5x +8 . . . . . . . . . . divide by °, collect terms

  3x = 24 . . . . . . . . . . add 16-5x

  x = 8 . . . . . . . . divide by 3

The measure of the angle of interest is ...

  ∠KLM = (8x-16)° = (8·8 -16)°

  ∠KLM = 48°

x=30

step-by-step explanation: