Question

pq is tangent to ⊙n. what is m∠n? 21° m∠n = °

Explanation:

Step1: Recall tangent - radius property

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

Step2: Use angle - sum property of a triangle

In $\triangle NPQ$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle{N}=x$, $\angle{Q} = 21^{\circ}$ and $\angle{NPQ}=90^{\circ}$. Then $x + 21^{\circ}+90^{\circ}=180^{\circ}$.

Step3: Solve for $\angle{N}$

$x=180^{\circ}-(90^{\circ} + 21^{\circ})$.
$x = 69^{\circ}$.

Answer:

$69$