aaron is standing at point c, watching his friends on a ferris wheel. he knows that he is looking up at a…

aaron is standing at point c, watching his friends on a ferris wheel. he knows that he is looking up at a 57° angle and the measure of arc bd is 80°. what is the measure of arc aed?

aaron is standing at point c, watching his friends on a ferris wheel. he knows that he is looking up at a 57° angle and the measure of arc bd is 80°. what is the measure of arc aed?

Answer

Answer:

$214$

Explanation:

Step1: Recall the secant - secant angle formula

The measure of an angle formed by two secants drawn from an external point to a circle is given by $\angle C=\frac{1}{2}(\text{major arc}-\text{minor arc})$. Here, $\angle C = 57^{\circ}$ and the minor arc is $\text{arc }BD=80^{\circ}$. Let the major arc be $\text{arc }AED$.

Step2: Set up the equation

Using the formula $\angle C=\frac{1}{2}(\text{arc }AED - \text{arc }BD)$, we substitute $\angle C = 57^{\circ}$ and $\text{arc }BD = 80^{\circ}$. So, $57^{\circ}=\frac{1}{2}(\text{arc }AED - 80^{\circ})$.

Step3: Solve the equation for arc AED

First, multiply both sides of the equation by 2: $2\times57^{\circ}=\text{arc }AED - 80^{\circ}$. Then, $114^{\circ}=\text{arc }AED - 80^{\circ}$. Add $80^{\circ}$ to both sides of the equation: $\text{arc }AED=114^{\circ}+ 100^{\circ}=214^{\circ}$.