Question

angle measures and segment lengths

solve for measure of angle a.

(14^{\circ})
(66^{\circ})

(a = ?^{\circ})

if 2 secant lines intersect outside a circle:
\\(\angle a = \frac{\widehat{c} - \widehat{b}}{2}\\)

Explanation:

Identify the given values

We are given a circle with two secant lines intersecting at an external point, forming an angle \(a\).
The intercepted arcs are:

• Farther arc (major arc) = \(66^\circ\)
• Nearer arc (minor arc) = \(14^\circ\)

State the applicable theorem

When two secants intersect outside a circle, the measure of the angle formed is half the difference of the measures of their intercepted arcs.
This is known as the Angles Outside Circle Theorem.
The formula is:

$$\angle a = \frac{\text{far arc} - \text{near arc}}{2}$$

Calculate the angle measure

Substitute the given arc measures into the formula:

$$a = \frac{66^\circ - 14^\circ}{2}$$

$$a = \frac{52^\circ}{2}$$

$$a = 26^\circ$$

Answer:

Solve for measure of angle a.

\(a =\) <blank>\(26\)</blank>\(^\circ\)