Question

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 right - hand side

\((9x - 10)+83=9x+(83 - 10)=9x + 73\), so the equation becomes \(127=9x + 73\)

Step4: Solve for \(x\)

Subtract 73 from both sides: \(127-73=9x+73 - 73\), which gives \(54 = 9x\). Then divide both sides by 9: \(x=\frac{54}{9}=6\)

Answer:

\(x = 6\)