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Answer 1 · 2018-05-22T17:54:36

#x=6#

We have #angle CDN cong angle CMN# because they subtend the same chord CD. It follows supplements #angle LDN cong angle LMC.#

#angle L# is congruent to itself so we have similar triangles #LDN \ ~ \ LMC.#

We write proportions #{LD}/{LN } = {LM}/{LC}#

# x /12 = 5/ ( x + 4)#

#x^2 + 4x - 60 = 0#

# (x + 10)(x-6) = 0#

#x = -10 or x=6#

We rule out #-10#

#x=6#

The proportion checks.