Question

1. if (mangle jkm = 43^{circ}), (mangle mkl=(8x - 20)^{circ}), and (mangle jkl=(10x - 11)^{circ}), find each measure.

Explanation:

Step1: Use angle - addition postulate

Since $\angle{JKM}+\angle{MKL}=\angle{JKL}$, we substitute the given angle measures: $43+(8x - 20)=10x-11$.

Step2: Simplify the left - hand side

$43+8x - 20=8x + 23$. So the equation becomes $8x + 23=10x-11$.

Step3: Solve for $x$

Subtract $8x$ from both sides: $23 = 10x-8x-11$, which simplifies to $23 = 2x-11$. Then add 11 to both sides: $23 + 11=2x$, so $34 = 2x$. Divide both sides by 2: $x = 17$.

Step4: Find $m\angle{MKL}$

Substitute $x = 17$ into the expression for $m\angle{MKL}$: $m\angle{MKL}=8x-20=8\times17-20=136 - 20=116^{\circ}$.

Step5: Find $m\angle{JKL}$

Substitute $x = 17$ into the expression for $m\angle{JKL}$: $m\angle{JKL}=10x-11=10\times17-11=170 - 11=159^{\circ}$.

Answer:

$x = 17$
$m\angle{MKL}=116^{\circ}$
$m\angle{JKL}=159^{\circ}$