Question

1. x = m∠jkl = m∠kjl = m∠klj = m∠klm = (5x - 27)° (7x - 32)° (9x - 8)°

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we set up the equation \((5x - 27)+(7x - 32)+(9x - 8)=180\).

Step2: Combine like - terms

\[

$$\begin{align*} (5x+7x + 9x)+(-27-32 - 8)&=180\\ 21x-67&=180 \end{align*}$$

\]

Step3: Isolate the variable term

Add 67 to both sides of the equation: \(21x=180 + 67\), so \(21x=247\).

Step4: Solve for x

Divide both sides by 21: \(x=\frac{247}{21}\approx11.76\).

Step5: Find the measure of each angle

• \(m\angle{JKL}=5x - 27=5\times\frac{247}{21}-27=\frac{1235}{21}-27=\frac{1235-567}{21}=\frac{668}{21}\approx31.81^{\circ}\)
• \(m\angle{KJL}=7x - 32=7\times\frac{247}{21}-32=\frac{1729}{21}-32=\frac{1729 - 672}{21}=\frac{1057}{21}\approx50.33^{\circ}\)
• \(m\angle{KLM}=9x - 8=9\times\frac{247}{21}-8=\frac{2223}{21}-8=\frac{2223-168}{21}=\frac{2055}{21}\approx97.86^{\circ}\)

Answer:

\(x=\frac{247}{21}\), \(m\angle{JKL}=\frac{668}{21}\), \(m\angle{KJL}=\frac{1057}{21}\), \(m\angle{KLM}=\frac{2055}{21}\)