Question

1. if (mangle mkl = 83^{circ}), (mangle jkl = 127^{circ}), and (mangle jkm=(9x - 10)^{circ}), find the value of (x).

Explanation:

Step1: Identify angle - relationship

We know that $m\angle{JKL}=m\angle{JKM}+m\angle{MKL}$.

Step2: Substitute given values

Substitute $m\angle{MKL} = 83^{\circ}$, $m\angle{JKL}=127^{\circ}$, and $m\angle{JKM}=(9x - 10)^{\circ}$ into the equation: $127=(9x - 10)+83$.

Step3: Simplify the equation

First, combine like - terms on the right - hand side: $127=9x-10 + 83$, which simplifies to $127=9x + 73$.

Step4: Solve for x

Subtract 73 from both sides of the equation: $127-73=9x+73 - 73$, so $54 = 9x$. Then divide both sides by 9: $\frac{54}{9}=x$, and $x = 6$.

Answer:

$x = 6$