Notice that both rays are secant to both circles. Use this to find m∠A and then to find x.
x=15^(∘)
Practice makes perfect
Let's begin by marking some points in the given diagram.
To find x we first have to find m∠A. We can do this by noticing that AB and AC are secant to the smaller circle and they intersect each other outside it. Thus, the measure of ∠A is one half the measure of the difference of the intercepted arcs.
m∠A = 1/2(m FG - m HI)
Next, let's substitute the given measures into the equation above.
Now that we know the measure of ∠A we apply the same reasoning as before, but this time we will use the bigger circle. Thus, the measure of ∠A equals one half the measure of the difference of the intercepted arcs.
m∠A = 1/2(m BC - m DE_(x^(∘)))
Finally, we substitute the corresponding values and find the value of x.
