Question

what is the value of x? h 58° 8x j

Explanation:

Step1: Recall circle - angle property

In a circle, if an inscribed - angle intercepts a diameter, the inscribed - angle is a right angle. So, in $\triangle HIJ$, $\angle I = 90^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle HIJ$, we know that $\angle H+\angle I+\angle J = 180^{\circ}$. Given $\angle H = 58^{\circ}$ and $\angle I = 90^{\circ}$, we can find $\angle J$.
$58^{\circ}+90^{\circ}+\angle J=180^{\circ}$
$\angle J=180^{\circ}-(58^{\circ} + 90^{\circ})=32^{\circ}$

Step3: Solve for $x$

Since $\angle J = 8x$, then $8x=32^{\circ}$.
Divide both sides by 8: $x=\frac{32^{\circ}}{8}=4^{\circ}$

Answer:

$4$