Question

finding an unknown angle measure
$overline{ab}$ is tangent to $odot c$ at point b and $overline{ad}$ is tangent to $odot c$ at point d.
what is $mangle a$
$\bigcirc$ $34^circ$
$\bigcirc$ $62^circ$
$\bigcirc$ $56^circ$
$\bigcirc$ $124^circ$

Explanation:

Step1: Recognize tangent-right angle property

A tangent to a circle forms a right angle with the radius at the point of tangency, so $m\angle ABC = 90^\circ$ and $m\angle ADC = 90^\circ$.

Step2: Use quadrilateral angle sum rule

The sum of interior angles of a quadrilateral is $360^\circ$. Let $m\angle A = x$.
$$x + 90^\circ + 124^\circ + 90^\circ = 360^\circ$$

Step3: Solve for $x$

Combine known angles: $90+124+90=304$. Rearrange to solve for $x$:
$$x = 360^\circ - 304^\circ$$
$$x = 56^\circ$$

Answer:

56° (Option C: 56°)