Step-by-step explanation:
[tex] \because \angle JKM [/tex] is the exterior angle of [tex] \triangle KLM [/tex]
[tex] \therefore [/tex] by remote interior angle theorem of a triangle, we have:
[tex] m\angle L + m\angle M = m\angle JKL \\\\
(18z + 3)\degree + (5z - 3)\degree = 161\degree \\\\
(18z + 3+5z - 3)\degree = 161\degree \\\\
(23z)\degree = 161\degree \\\\
23z = 161\\\\
z = \frac{161}{23} \\\\
\huge \red {\boxed {z = 7}} \\\\
\because \measuredangle L = (18z +3)\degree \\\\
\therefore \measuredangle L = (18\times 7+3)\degree \\\\
\therefore \measuredangle L = (126+3)\degree \\\\
\huge\purple {\boxed {\therefore \measuredangle L = 129\degree}} \\\\
\because \measuredangle M = (5z - 3)\degree \\\\
\therefore \measuredangle M= (5\times 7-3)\degree \\\\
\therefore \measuredangle M = (35-3)\degree \\\\
\huge\orange {\boxed {\therefore \measuredangle M = 32\degree}} \\\\[/tex]
