Question

np is tangent to ⊙m. what is m∠p? m∠p =

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pythagorean theorem (100)
lesson: tangent to a circle

Explanation:

Step1: Recall tangent - radius property

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

Step2: Use angle - sum property of a triangle

In $\triangle MNP$, the sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle P=x$, $m\angle M = 46^{\circ}$ and $m\angle N=90^{\circ}$. Then $x + 90^{\circ}+46^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle P$

$x=180^{\circ}-(90^{\circ} + 46^{\circ})=44^{\circ}$.

Answer:

$44$