Question

Find the value of z. Then find the value of the interior angles ​

Answer 1

Explanation:

`\because \angle JKM` is the exterior angle of
`\triangle KLM`

`\therefore` by remote interior angle theorem of a triangle, we have:

`m\angle L + m\angle M = m\angle JKL \\\\</p><p>(18z + 3)\degree + (5z - 3)\degree = 161\degree \\\\</p><p>(18z + 3+5z - 3)\degree = 161\degree \\\\</p><p>(23z)\degree = 161\degree \\\\</p><p>23z = 161\\\\</p><p>z = (161)/(23) \\\\</p><p>\huge \red {\boxed {z = 7}} \\\\</p><p>\because \measuredangle L = (18z +3)\degree \\\\</p><p>\therefore \measuredangle L = (18* 7+3)\degree \\\\</p><p>\therefore \measuredangle L = (126+3)\degree \\\\</p><p></p><p>\huge\purple {\boxed {\therefore \measuredangle L = 129\degree}} \\\\</p><p></p><p>\because \measuredangle M = (5z - 3)\degree \\\\</p><p>\therefore \measuredangle M= (5* 7-3)\degree \\\\</p><p>\therefore \measuredangle M = (35-3)\degree \\\\</p><p></p><p>\huge\orange {\boxed {\therefore \measuredangle M = 32\degree}} \\\\`