The problem presents a circle with center D. Two chords, AB and AC, are drawn from point A. The measure of arc BC is not given, but the measures of arc AB and arc AC are both given as 129 degrees. The expressions for the length of the chords AB and AC are given in terms of $x$ as $4x + 3$ and $2x + 21$ respectively. We are asked to find the value of $x$.

1. Problem Description

The problem presents a circle with center D. Two chords, AB and AC, are drawn from point A. The measure of arc BC is not given, but the measures of arc AB and arc AC are both given as 129 degrees. The expressions for the length of the chords AB and AC are given in terms of $x$ as $4x + 3$ and $2x + 21$ respectively. We are asked to find the value of $x$.

2. Solution Steps

Since the measure of arcs AB and AC are equal, the chords AB and AC must also be equal in length. Therefore, we can set the expressions for the lengths of the chords equal to each other and solve for $x$.

$4x + 3 = 2x + 21$

Subtract $2x$ from both sides:

$4x - 2x + 3 = 2x - 2x + 21$

$2x + 3 = 21$

Subtract 3 from both sides:

$2x + 3 - 3 = 21 - 3$

$2x = 18$

Divide both sides by 2:

$\frac{2x}{2} = \frac{18}{2}$

$x = 9$

3. Final Answer

The value of $x$ is 9.