Question

1. if m∠mkl = 83°, m∠jkl = 127°, and m∠jkm=(9x - 10)°, find the value of x.

Explanation:

Step1: Identify angle - addition 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

First, simplify the right - hand side of the equation: \((9x - 10)+83=9x+(83 - 10)=9x + 73\). So the equation becomes \(127=9x + 73\).

Step4: Solve for \(x\)

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

Answer:

\(x = 6\)