Question

find the measure of arc b.
130°
b° 47°
b = ?°

Explanation:

Step1: Recall external secant angle formula

The measure of an angle formed by two secants drawn from a point outside the circle is half the difference of the measures of the intercepted arcs. The formula is:
$$\text{Angle} = \frac{1}{2} \times (\text{Major Arc} - \text{Minor Arc})$$

Step2: Substitute known values

Let the major arc be $130^\circ$, the angle be $47^\circ$, and the minor arc be $b^\circ$. Substitute into the formula:
$$47 = \frac{1}{2} \times (130 - b)$$

Step3: Solve for $b$

Multiply both sides by 2:
$$94 = 130 - b$$
Rearrange to isolate $b$:
$$b = 130 - 94$$

Answer:

$36^\circ$