Answer:
x = 9 and ∠ JKM = 59°.
Step-by-step explanation:
See the attached diagram with this question.
∠ JKL is bisected by line KM.
Therefore, angle JKM = angle MKL
Now, ∠ JKM is given to be ( x² - 22 ) and ∠ LKM = ( 6x + 5 ).
So, x² - 22 = 6x + 5
⇒ x² - 6x -27 = 0
⇒ ( x - 9 ) ( x + 3 ) = 0
Therefore, x = 9 or - 3.
∠ JKM = x² - 22 = 59° for x = 9 and ∠ JKM = x² - 22 = - 13° for x = - 3
Since angle JKM can not be negative, so, x = 9 and ∠ JKM = 59°. (Answer)
