Question

PLEASE HELP ME ASAP!!!! (I included the picture below with the question!!!)

Answer 1

Answer:

$x=30^o$

Step-by-step explanation:

step 1

Find the measure of angle KNL

we know that

$m\angle KNL+m\angle LNM+m\angle ONM=180^o$----> by straight angle

we have

$m\angle LNM=45^o$ ---> given problem

$m\angle ONM=105^o$ ---> given problem

substitute the given values

$m\angle KNL+45^o+105^o=180^o$

$m\angle KNL+150^o=180^o$

$m\angle KNL=180^o-150^o$

$m\angle KNL=30^o$

step 2

Find the value of x

In the right triangle KNL

we know that

$m\angle KNL+m\angle NKL=90^o$ ----> by complementary angles

we have

$m\angle KNL=30^o$

$m\angle NKL=2x$

substitute

$30^o+2x=90^o$

$2x=90^o-30^o$

$2x=60^o$

$x=30^o$