Question

find the measure of arc b.
115°
b° 41°
b = ?°

Explanation:

Step1: Recall external secant angle formula

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

Step2: Substitute known values

We know the external angle is $41^\circ$, the major intercepted arc is $115^\circ$, and the minor arc is $b^\circ$. Plug these into the formula:
$$41 = \frac{1}{2}(115 - b)$$

Step3: Solve for $b$

Multiply both sides by 2:
$$82 = 115 - b$$
Rearrange to isolate $b$:
$$b = 115 - 82$$
$$b = 33$$

Answer:

$33^\circ$