Question

additional details were added for this assignment.
$overleftrightarrow{cd}$ is tangent to circle $a$ at point $b$.
what is the measure of $angle abd$?
$\circ\\ 45^\circ$
$\circ\\ 60^\circ$
$\circ\\ 90^\circ$
$\circ\\ 180^\circ$
diagram of circle $a$, tangent line $cd$ at point $b$, with points $d$, $c$, $b$ on the tangent, and lines from $a$ to $b$, $a$ to $c$, $a$ to $d$

Explanation:

Step1: Recall Tangent-Radius Theorem

The tangent to a circle is perpendicular to the radius at the point of tangency. So, \( AB \) is the radius and \( CD \) is the tangent at \( B \), so \( AB \perp CD \).

Step2: Determine \( \angle ABD \)

Since \( AB \perp CD \), the angle between them (\( \angle ABD \)) is \( 90^\circ \).

Answer:

\( 90^\circ \) (corresponding to the option with \( 90^\circ \))