Question

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?

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 $\angle C=\frac{1}{2}(\text{measure of arc AED}-\text{measure of arc BD})$.

Step2: Substitute the given values

We know that $\angle C = 57^{\circ}$ and the measure of arc $BD=80^{\circ}$. Substituting into the formula $57^{\circ}=\frac{1}{2}(x - 80^{\circ})$, where $x$ is the measure of arc $AED$.

Step3: Solve for $x$

First, multiply both sides of the equation by 2: $2\times57^{\circ}=x - 80^{\circ}$. So, $114^{\circ}=x - 80^{\circ}$. Then, add $80^{\circ}$ to both sides: $x=114^{\circ}+80^{\circ}=194^{\circ}$.

Answer:

$194$