Answer:
Therefore, x = 23°, ∠LKM = 56° and ∠MKN = 89° .
Step-by-step explanation:
Given that ∠LKN is 145° so we can assume that ∠LKM addes together with ∠MKN will get 145° in terms of x :
[tex]∠lkn = ∠lkm + ∠mkn = 145[/tex]
[tex]2x + 10 + 4x - 3 = 145[/tex]
[tex]6x + 7 = 145[/tex]
[tex]6x = 145 - 7[/tex]
[tex]6x = 138[/tex]
[tex]x = 138 \div 6 = 23[/tex]
Next, we have to substitute x = 23° into the expressions of ∠LKM and ∠MKN :
[tex]∠lkm = 2(23) + 10 = 56[/tex]
[tex]∠mkn = 4(23) - 3 = 89[/tex]
