Find the measure of angle 1, denoted as $m\angle 1$. We are given that the arc $AC$ has a measure of $71^\circ$ and the arc $DB$ has a measure of $82^\circ$.

1. Problem Description

Find the measure of angle 1, denoted as $m\angle 1$. We are given that the arc $AC$ has a measure of $71^\circ$ and the arc $DB$ has a measure of $82^\circ$.

2. Solution Steps

The measure of an angle formed by two chords intersecting inside a circle is equal to one-half the sum of the intercepted arcs.

In this case, $\angle 1$ is formed by the intersection of chords $AD$ and $BC$. The intercepted arcs are $AC$ and $DB$.

Therefore, the measure of $\angle 1$ is given by

$m\angle 1 = \frac{1}{2}(m\text{arc }AC + m\text{arc }DB)$

$m\angle 1 = \frac{1}{2}(71^\circ + 82^\circ)$

$m\angle 1 = \frac{1}{2}(153^\circ)$

$m\angle 1 = 76.5^\circ$

3. Final Answer

7

6. 5°