Question

1. if m∠mkl = 83°, m∠jkl = 127°, and m∠jkm=(9x - 10)°, find the value of x.
2. if m∠efh=(5x + 1)°, m∠hfg = 62°, and m∠efg=(18x + 11)°, find each measure.

Explanation:

Step1: Use angle - addition postulate

We know that \(m\angle JKL=m\angle JKM + m\angle MKL\). So, \((9x - 10)+83 = 127\).

Step2: Simplify the left - hand side

\(9x-10 + 83=9x + 73\). So the equation becomes \(9x+73 = 127\).

Step3: Solve for \(x\)

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

Answer:

\(x = 6\)