#### Answer

An angle with its vertex at the center of a circle that intercepts an arc on the circle double in length to the radius of the circle has a measure of 2 radians.

#### Work Step by Step

'An angle with its vertex at the center of a circle that intercepts an arc on the circle double in length to the radius of the circle has a measure of 2 radians.'
To prove this, we assume the radius $r$ to be $x$. This means the arc length $s$ would then be $2x$.
Substituting these values in $\theta=\frac{s}{r}$:
$\theta=\frac{s}{r}=\frac{2x}{x}=2$ radians
Hence proved that an angle with its vertex at the center of a circle that intercepts an arc on the circle double in length to the radius of the circle has a measure of 2 radians.