Let's solve this geometry problem step-by-step.
1. Understand the Problem:
- Angle [tex]\( ABC \)[/tex] measures [tex]\( 50^\circ \)[/tex].
- Line segment [tex]\( AD \)[/tex] bisects [tex]\( \angle ABC \)[/tex], meaning it divides [tex]\( \angle ABC \)[/tex] into two equal smaller angles.
- One of these smaller angles is represented as [tex]\( 2x + 1 \)[/tex] degrees.
- We need to determine the value of [tex]\( x \)[/tex].
2. Determine the Measure of the Smaller Angles:
Since [tex]\( AD \)[/tex] bisects [tex]\( \angle ABC \)[/tex], each smaller angle will be half of [tex]\( \angle ABC \)[/tex]:
[tex]\[
\text{Measure of each smaller angle} = \frac{\angle ABC}{2} = \frac{50^\circ}{2} = 25^\circ
\][/tex]
3. Set Up the Equation:
Given that one of these smaller angles is represented by [tex]\( 2x + 1 \)[/tex] degrees, we can set up the following equation:
[tex]\[
2x + 1 = 25
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Subtract 1 from both sides of the equation:
[tex]\[
2x = 25 - 1
\][/tex]
[tex]\[
2x = 24
\][/tex]
- Divide both sides by 2:
[tex]\[
x = \frac{24}{2}
\][/tex]
[tex]\[
x = 12
\][/tex]
5. Conclusion:
The value of [tex]\( x \)[/tex] is [tex]\( \boxed{12} \)[/tex].
By following the steps and solving the equation, we determined that the value of [tex]\( x \)[/tex] is [tex]\( 12 \)[/tex].
