Question

in circle o, what is mae? 84° 96° 120° 168°

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 $\frac{1}{2}(m\overparen{major\ arc}-m\overparen{minor\ arc})$. Here, $\angle C=\frac{1}{2}(m\overparen{AE}-m\overparen{BD})$.

Step2: Substitute the known values

We know that $\angle C = 36^{\circ}$ and $m\overparen{BD}=48^{\circ}$. So, $36^{\circ}=\frac{1}{2}(m\overparen{AE}- 48^{\circ})$.

Step3: Solve for $m\overparen{AE}$

First, multiply both sides of the equation by 2: $2\times36^{\circ}=m\overparen{AE}-48^{\circ}$. Then, $72^{\circ}=m\overparen{AE}-48^{\circ}$. Add $48^{\circ}$ to both sides: $m\overparen{AE}=72^{\circ}+48^{\circ}=120^{\circ}$.

Answer:

$120^{\circ}$ (corresponding to the option "120°")