Question

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

Explanation:

Step1: Use angle addition postulate

According to the angle addition postulate, \(m\angle JKM + m\angle MKL=m\angle JKL\).
Substitute the given values: \((9x - 10)+83 = 127\).

Step2: Simplify the left - hand side

Combine like terms: \(9x+( - 10 + 83)=127\), so \(9x + 73=127\).

Step3: Solve for \(x\)

Subtract 73 from both sides: \(9x=127 - 73\), \(9x = 54\).
Divide both sides by 9: \(x=\frac{54}{9}\).

Answer:

\(x = 6\)