Question

problem 19: (first taught in lesson 12) if $overrightarrow{oj}$ bisects $angle iok$, and if $mangle ioj = 5x + 2$ and $mangle jok = 6x - 9$, then find $mangle ioj$. after you enter your answer press go. $mangle ioj = $

Explanation:

Step1: Set up equation

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

Step2: Solve for x

Subtract $5x$ from both sides: $2=x - 9$. Then add 9 to both sides, getting $x = 11$.

Step3: Find $m\angle IOJ$

Substitute $x = 11$ into the expression for $m\angle IOJ$: $m\angle IOJ=5\times11 + 2=55+2 = 57$.

Answer:

57