Question

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

Explanation:

Step1: Recall tangent - radius property

A 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: Consider the quadrilateral ABCD

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

Step3: Solve for $\angle A$

Simplify the equation:
\[

$$\begin{align*} x+304^{\circ}&=360^{\circ}\\ x&=360^{\circ}- 304^{\circ}\\ x&=56^{\circ} \end{align*}$$

\]

Answer:

$56^{\circ}$