Question

lines cd and de are tangent to circle a, as shown below: if $overset{\frown}{ce}$ is 125°, what is the measure of $angle cde? 55° 62.5° 117.5° 125° question 8 (multiple choice worth 1 points)

Explanation:

Step1: Recall the property of angles related to tangents and arcs

The measure of the angle formed by two tangents to a circle is half the difference of the measures of the intercepted arcs. The sum of the major - arc and the minor - arc of a circle is 360°. Given the minor - arc $\overset{\frown}{CE}=125^{\circ}$, then the major - arc $\overset{\frown}{CBE}=360^{\circ}- 125^{\circ}=235^{\circ}$.

Step2: Apply the formula for the angle between two tangents

The formula for the measure of the angle $\angle CDE$ formed by two tangents $CD$ and $DE$ is $\angle CDE=\frac{1}{2}(\text{major arc}-\text{minor arc})$. Substitute the values of the major and minor arcs: $\angle CDE=\frac{1}{2}(235^{\circ}-125^{\circ})$.

Step3: Calculate the value of $\angle CDE$

First, calculate the value inside the parentheses: $235^{\circ}-125^{\circ}=110^{\circ}$. Then, $\frac{1}{2}\times110^{\circ}=55^{\circ}$.

Answer:

A. $55^{\circ}$