Question

determining a formula
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 angle - outside - circle formula

The measure of an angle formed by two secants, two tangents, or a secant and a tangent outside a circle is half the positive difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

For the given angle 1, the intercepted arcs are the arcs with measures \(a^{\circ}\) and \(b^{\circ}\).

Step3: Apply the formula

The formula for the measure of an angle formed by a secant and a tangent outside a circle is \(\frac{1}{2}(a - b)\) where \(a\) is the measure of the larger - intercepted arc and \(b\) is the measure of the smaller - intercepted arc.

Answer:

\(\frac{1}{2}(a^{\circ}-b^{\circ})\)