Question

the measure of m∠jml is 85°. select all the true statements.

a. m∠jmk = 10°
b. m∠kml = 11°
c. m∠jmk = 50°
d. m∠kml = 35°
e. m∠jmk + m∠kml = m∠jml

Explanation:

Step1: Set up an equation based on angle - addition

Since $\angle JML=\angle JMK+\angle KML$, we have $(6x + 2)+(4x + 3)=85$.

Step2: Combine like - terms

$6x+4x+2 + 3=85$, which simplifies to $10x+5 = 85$.

Step3: Solve for $x$

Subtract 5 from both sides: $10x=85 - 5=80$. Then divide both sides by 10, so $x = 8$.

Step4: Find the measure of $\angle JMK$

Substitute $x = 8$ into the expression for $\angle JMK$: $m\angle JMK=6x + 2=6\times8+2=48 + 2=50^{\circ}$.

Step5: Find the measure of $\angle KML$

Substitute $x = 8$ into the expression for $\angle KML$: $m\angle KML=4x + 3=4\times8+3=32 + 3=35^{\circ}$.

Step6: Check the statements

• For statement A: $m\angle JMK = 10^{\circ}$ is false.
• For statement B: $m\angle KML = 11^{\circ}$ is false.
• For statement C: $m\angle JMK = 50^{\circ}$ is true.
• For statement D: $m\angle KML = 35^{\circ}$ is true.
• For statement E: Since $\angle JML=\angle JMK+\angle KML$, $m\angle JMK + m\angle KML=m\angle JML$ is true.

Answer:

C. $m\angle JMK = 50^{\circ}$
D. $m\angle KML = 35^{\circ}$
E. $m\angle JMK + m\angle KML=m\angle JML$