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 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 given by half the difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

For the given angle 1 formed by a secant and a tangent, the intercepted arcs are the larger arc with measure \(a^{\circ}\) and the smaller arc with measure \(b^{\circ}\).

Step3: Apply the formula

The measure of angle 1 is \(\frac{1}{2}(a^{\circ}-b^{\circ})\).

Answer:

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