Question

which formula would be used to find the measure of angle 1?
$\frac{1}{2}(a^circ + b^circ)$.
$\frac{1}{2}(a^circ - c^circ)$.
$\frac{1}{2}(b^circ + c^circ)$.
$\frac{1}{2}(a^circ - b^circ)$.

Explanation:

Step1: Recall exterior angle theorem

When an angle is formed outside a circle by two secants, its measure is half the difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

Angle 1 is formed outside the circle. The larger intercepted arc is $a^\circ$, the smaller intercepted arc is $c^\circ$.

Step3: Apply the theorem

The formula for the measure of angle 1 is half the difference of the larger arc and the smaller arc.
<Expression>
$\text{Measure of } \angle 1 = \frac{1}{2}(a^\circ - c^\circ)$
</Expression>

Answer:

$\boldsymbol{\frac{1}{2}(a^\circ - c^\circ)}$ (the second option)