Question

in the diagram of circle o, what is the measure of ∠abc? 34° 45° 68° 73°

Explanation:

Step1: Recall external tangent angle formula

The measure of an angle formed by two tangents to a circle is half the difference of the measures of the intercepted arcs. The major arc \(AC\) is \(360^\circ - 146^\circ = 214^\circ\), the minor arc \(AC\) is \(146^\circ\).

Step2: Calculate \(\angle ABC\)

$$ m\angle ABC = \frac{1}{2} \times (214^\circ - 146^\circ) $$

$$ m\angle ABC = \frac{1}{2} \times 68^\circ = 34^\circ $$

Answer:

34°