Question

the measure of $m\angle jml$ is $85^\circ$. select all the true statements.$(6x + 2)^\circ$$(4x + 3)^\circ$a. $m\angle jmk = 10^\circ$b. $m\angle kml = 11^\circ$c. $m\angle jmk = 50^\circ$d. $m\angle kml = 35^\circ$e. $m\angle jmk - m\angle kml = m\angle jml$

Explanation:

Step1: Set up angle sum equation

$\angle JML = \angle JMK + \angle KML$
$85^\circ = (6x+2)^\circ + (4x+3)^\circ$

Step2: Simplify and solve for x

Combine like terms: $85 = 10x + 5$
Isolate x: $10x = 85 - 5 = 80$
$x = \frac{80}{10} = 8$

Step3: Calculate $\angle JMK$

Substitute $x=8$: $\angle JMK = 6(8)+2 = 50^\circ$

Step4: Calculate $\angle KML$

Substitute $x=8$: $\angle KML = 4(8)+3 = 35^\circ$

Step5: Verify statement E

Check $\angle JMK + \angle KML = 50+35=85^\circ = \angle JML$, so E's expression is incorrect.

Answer:

C. $m\angle JMK = 50^\circ$
D. $m\angle KML = 35^\circ$