Question

In the diagram, −→− bisects ∠ .

Answer 1

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)