Question

jk is tangent to ⊙h. what is the value of x? x =

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle HJK = 90^{\circ}$. In $\triangle HJK$, we know that the sum of the interior angles of a triangle is $180^{\circ}$.

Step2: Set up an equation

We have $\angle K=31^{\circ}$, $\angle HJK = 90^{\circ}$, and $\angle JHK=8x - 5^{\circ}$. Using the angle - sum property of a triangle ($\angle K+\angle JHK+\angle HJK = 180^{\circ}$), we substitute the values: $31+(8x - 5)+90 = 180$.

Step3: Simplify the equation

First, combine like - terms: $31-5 + 90+8x=180$. So, $116 + 8x=180$.

Step4: Solve for x

Subtract 116 from both sides of the equation: $8x=180 - 116$. Then $8x = 64$. Divide both sides by 8: $x=\frac{64}{8}=8$.

Answer:

$8$