Question

jl bisects ∠ljk. if m∠jlk = (-6x + 16)° and m∠ljk=(44 - 6x)°, find the requested values. x = m∠ljk =

Explanation:

Step1: Recall angle - bisector property

If a ray bisects an angle, the measure of the two resulting sub - angles are equal. So, \(m\angle ILJ=\frac{1}{2}m\angle IJK\). Since \(m\angle ILJ = (- 6x + 16)^{\circ}\) and \(m\angle IJK=(44 - 6x)^{\circ}\), we have \(2(-6x + 16)=44 - 6x\).

Step2: Expand the left - hand side

\[

$$\begin{align*} 2(-6x + 16)&=44 - 6x\\ -12x+32&=44 - 6x \end{align*}$$

\]

Step3: Add \(12x\) to both sides

\[

$$\begin{align*} -12x + 12x+32&=44 - 6x+12x\\ 32&=44 + 6x \end{align*}$$

\]

Step4: Subtract 44 from both sides

\[

$$\begin{align*} 32-44&=44 - 44+6x\\ -12&=6x \end{align*}$$

\]

Step5: Solve for \(x\)

\[

$$\begin{align*} x&=\frac{-12}{6}\\ x&=- 2 \end{align*}$$

\]

Step6: Find \(m\angle IJK\)

Substitute \(x = - 2\) into the expression for \(m\angle IJK\): \(m\angle IJK=44-6x=44-6\times(-2)=44 + 12 = 56^{\circ}\)

Answer:

\(x=-2\)
\(m\angle IJK = 56^{\circ}\)