Question

ab is tangent to ⊙c at point b and ad is tangent to ⊙c at point d. what is m∠a? 34° 62° 56° 124°

Explanation:

Step1: Recall tangent - radius property

Tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle ABC = 90^{\circ}$ and $\angle ADC=90^{\circ}$.

Step2: Use the sum of angles in a quadrilateral

The sum of the interior angles of a quadrilateral $ABCD$ is $360^{\circ}$. In quadrilateral $ABCD$, we know $\angle ABC = 90^{\circ}$, $\angle ADC = 90^{\circ}$ and $\angle BCD=124^{\circ}$. Let $\angle BAD = x$. Then $x + 90^{\circ}+90^{\circ}+124^{\circ}=360^{\circ}$.

Step3: Solve for $\angle BAD$

$x=360^{\circ}-(90^{\circ}+90^{\circ}+124^{\circ})=360^{\circ}-304^{\circ}=56^{\circ}$. So, $m\angle A = 56^{\circ}$.

Answer:

$56^{\circ}$