Question

if \\( \overrightarrow { o j } \\) bisects \\( \angle i o k \\), and if \\( m \angle i o j = 5 x + 2 \\) and \\( m \angle j o k = 6 x - 9 \\), then find \\( m \angle i o j \\).
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\\( m \angle i o j = \\)

Explanation:

Step1: Use the angle - bisector property

Since \(\overrightarrow{OJ}\) bisects \(\angle IOK\), then \(m\angle IOJ=m\angle JOK\). So, \(5x + 2=6x-9\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(2=x - 9\).
Add \(9\) to both sides: \(x=2 + 9=11\).

Step3: Find \(m\angle IOJ\)

Substitute \(x = 11\) into \(m\angle IOJ=5x+2\). Then \(m\angle IOJ=5\times11+2=55 + 2=57\).

Answer:

\(57\)