Question

secants, tangents, and angles in circle o, what is mae? 84° 96° 168° 120°

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 $\angle C=\frac{1}{2}(m\overparen{AE}-m\overparen{BD})$.

Step2: Substitute the known values

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

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

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

Answer:

$120^{\circ}$