Answer:
[tex]x=30^o[/tex]
Step-by-step explanation:
step 1
Find the measure of angle KNL
we know that
[tex]m\angle KNL+m\angle LNM+m\angle ONM=180^o[/tex]----> by straight angle
we have
[tex]m\angle LNM=45^o[/tex] ---> given problem
[tex]m\angle ONM=105^o[/tex] ---> given problem
substitute the given values
[tex]m\angle KNL+45^o+105^o=180^o[/tex]
[tex]m\angle KNL+150^o=180^o[/tex]
[tex]m\angle KNL=180^o-150^o[/tex]
[tex]m\angle KNL=30^o[/tex]
step 2
Find the value of x
In the right triangle KNL
we know that
[tex]m\angle KNL+m\angle NKL=90^o[/tex] ----> by complementary angles
we have
[tex]m\angle KNL=30^o[/tex]
[tex]m\angle NKL=2x[/tex]
substitute
[tex]30^o+2x=90^o[/tex]
[tex]2x=90^o-30^o[/tex]
[tex]2x=60^o[/tex]
[tex]x=30^o[/tex]
