Question

jb bisects ∠ijk. find m∠ijb if m∠bjk=(3x - 5)° and m∠ijb=(x + 37)°. x= m∠ijb=

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{JB}$ bisects $\angle IJK$, then $m\angle IJB=m\angle BJK$. So we set up the equation $x + 37=3x-5$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $37 = 3x - x-5$, which simplifies to $37=2x - 5$. Then add 5 to both sides: $37 + 5=2x$, so $42 = 2x$. Divide both sides by 2: $x=\frac{42}{2}=21$.

Step3: Find $m\angle IJB$

Substitute $x = 21$ into the expression for $m\angle IJB$. We have $m\angle IJB=x + 37$. So $m\angle IJB=21+37=58^{\circ}$.

Answer:

$x = 21$
$m\angle IJB=58^{\circ}$