Okay, so I was reading the definition of Angles. It says the following:
Draw an imaginary circle around the vertex. The angle is the portion of the imaginary circle captured (subtended) by the rays. No matter how small or large you draw your circle the fraction of the circle captured (subtended) by the rays would be the same. For example, if the angle is measured using degrees, and the angle shown is $50$ degrees, then no matter how large or small you draw your imaginary circle around the vertex, then you get $50$ degrees out of $360$ degrees (whole circle). Using distance to measure the same thing is arc measure, which measures a specific arc a part of a specific circle drawn a specific distance from the vertex. Draw a small circle, get a smaller distance. Draw a larger circle and the distance gets greater. These are two different measurements and two different things.
No matter how small or large you draw your circle the fraction of the circle captured (subtended) by the rays would be the same.
How to prove this statement?
Are angles really defined this way?
$$\text{Area of Circle}=\pi r^2$$ $$\text{Area of Sector}=\pi r^2\cdot\frac{\theta}{360}$$ $$\text{Fraction of Circle}=\frac{\text{Area of Sector}}{\text{Area of Circle}}=\frac{\theta}{360}$$ As you can see, the fraction of the circle is only dependent on the angle and independent of the radius of the circle. Hence Proved.