Question

angle measures and segment lengths

solve for measure of angle a.

(124^{\circ})
(36^{\circ})
a

(a = ?^{\circ})

if two chords intersect inside a circle:
\\(\angle a = \frac{\widehat{b} + \widehat{c}}{2}\\)

Explanation:

Identify the given values and formula

The problem asks to solve for the measure of angle \(a\), which is formed by two intersecting chords inside a circle.
The intercepted arcs are given as:

• One intercepted arc: \(36^\circ\)
• The opposite intercepted arc: \(124^\circ\)

The formula provided in the image is:

$$\angle a = \frac{b + c}{2}$$

where \(b\) and \(c\) are the measures of the intercepted arcs.

Substitute the values into the formula

Substitute \(b = 36^\circ\) and \(c = 124^\circ\) into the formula:

$$a = \frac{36 + 124}{2}$$

Calculate the final value

Calculate the sum and divide by 2:

$$a = \frac{160}{2} = 80$$

Answer:

Solve for measure of angle a.

\(a =\) <blank>80</blank>\(^\circ\)