Question

$\overleftrightarrow{ab}$ is tangent to circle $d$.
what is $m\angle abc$?
$\circ$
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Explanation:

Step1: Identify tangent-radius right angle

$\angle ABD = 90^\circ$ (tangent $\overleftrightarrow{AB}$ is perpendicular to radius $DB$)

Step2: Find base angles of $\triangle DBC$

Since $DB=DC$ (radii of the same circle), $\triangle DBC$ is isosceles.
Let $\angle DBC = \angle DCB = x$.
Sum of angles in a triangle: $113^\circ + x + x = 180^\circ$
$2x = 180^\circ - 113^\circ = 67^\circ$
$x = \frac{67^\circ}{2} = 33.5^\circ$

Step3: Calculate $\angle ABC$

$\angle ABC = \angle ABD - \angle DBC$
$\angle ABC = 90^\circ - 33.5^\circ$

Answer:

$56.5^\circ$