Question

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

Explanation:

Step1: Recall the formula for the measure of an angle formed by two secants

The measure of an angle formed by two secants outside a circle is \(\frac{1}{2}\) (difference of the measures of the intercepted arcs).

Step2: Identify the intercepted arcs

The intercepted arcs for angle \(1\) are \(a^{\circ}\) and \(b^{\circ}\)

Answer:

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