Question

jh bisects ∠vjs.
if ∠hjs = 26x and ∠vjs = 53x - 2
x =
∠hjs =

Explanation:

Step1: Recall angle - bisector property

Since $\overline{JH}$ bisects $\angle VJS$, then $\angle VJH=\angle HJS$. And $\angle VJS=\angle VJH + \angle HJS = 2\angle HJS$.

Step2: Set up an equation

We know that $\angle HJS = 26x$ and $\angle VJS=53x - 2$. Since $\angle VJS = 2\angle HJS$, we substitute the expressions: $53x-2 = 2\times(26x)$.

Step3: Solve the equation

Expand the right - hand side: $53x-2 = 52x$. Subtract $52x$ from both sides: $53x-52x-2=52x - 52x$, which gives $x - 2=0$. Then add 2 to both sides, so $x = 2$.

Step4: Find $\angle HJS$

Substitute $x = 2$ into the expression for $\angle HJS$. $\angle HJS=26x$, so $\angle HJS=26\times2=52^{\circ}$.

Answer:

$x = 2$
$\angle HJS = 52^{\circ}$