Question

question 2 of 5
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segment ab is tangent to the circle at point a. what is the measure of ∠abc?
m∠abc = □ °

Explanation:

Step1: Recall the tangent - secant angle formula

The measure of an angle formed by a tangent and a secant is half the difference of the intercepted arcs.
The two intercepted arcs are the major arc and the minor arc. Here, the major arc is $175^{\circ}$ and the minor arc is $85^{\circ}$.

Step2: Apply the formula

The formula for the measure of $\angle ABC$ (where $AB$ is tangent and $BCD$ is secant) is $m\angle ABC=\frac{1}{2}(\text{major arc}-\text{minor arc})$.
Substitute the values of the arcs: $m\angle ABC=\frac{1}{2}(175 - 85)$.
First, calculate the difference inside the parentheses: $175-85 = 90$.
Then, find half of the difference: $\frac{1}{2}\times90=45$.

Answer:

$45$