Question

find ∠jmk, if the measure of ∠jml is 113°. ∠jmk =

Explanation:

Step1: Set up an equation

Since $\angle JML=\angle JMK+\angle KML$, we have $113=(10z + 107)+(7z + 74)$.

Step2: Combine like - terms

$113 = 10z+7z + 107+74$, which simplifies to $113=17z + 181$.

Step3: Solve for z

Subtract 181 from both sides: $113 - 181=17z$, so $- 68 = 17z$. Then divide both sides by 17: $z=-4$.

Step4: Find $\angle JMK$

Substitute $z = - 4$ into the expression for $\angle JMK$ which is $10z + 107$. So $\angle JMK=10\times(-4)+107$.
$\angle JMK=-40 + 107=67^{\circ}$.

Answer:

$67^{\circ}$