Question

$\overleftrightarrow{jk}$ is tangent to $\odot h$. what is $m\angle h$?
$m\angle h = \square^\circ$

Explanation:

Step1: Use the property of tangent - radius

A tangent to a circle is perpendicular to the radius at the point of tangency. So, \( \angle HJK = 90^{\circ}\).

Step2: Use the angle - sum property of a triangle

In \(\triangle HJK\), we know that the sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle H=x\), \(m\angle K = 20^{\circ}\), and \(m\angle HJK=90^{\circ}\).
By the angle - sum formula \(m\angle H+m\angle K + m\angle HJK=180^{\circ}\), we substitute the values: \(x + 20^{\circ}+90^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Simplify the equation \(x+110^{\circ}=180^{\circ}\). Subtract \(110^{\circ}\) from both sides: \(x=180^{\circ}-110^{\circ}\).

Answer:

\(70\)