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 is half the difference of the measures of the intercepted arcs. Let the measure of arc $AE$ be $x$ and the measure of the other intercepted arc (the smaller one) be $48^{\circ}$. The angle $\angle C = 36^{\circ}$. The formula is $\angle C=\frac{1}{2}(x - 48^{\circ})$.

Step2: Solve for $x$

We have the equation $36^{\circ}=\frac{1}{2}(x - 48^{\circ})$. First, multiply both sides of the equation by 2: $2\times36^{\circ}=x - 48^{\circ}$. So, $72^{\circ}=x - 48^{\circ}$. Then add $48^{\circ}$ to both sides of the equation: $x=72^{\circ}+ 48^{\circ}=120^{\circ}$.

Answer:

$120^{\circ}$