The problem asks us to calculate the peripheral angle (also known as the inscribed angle) above a circular arc that is equal to $1/12$ of the circle.

1. Problem Description

The problem asks us to calculate the peripheral angle (also known as the inscribed angle) above a circular arc that is equal to $1/12$ of the circle.

2. Solution Steps

The peripheral angle is half the central angle that subtends the same arc.

A full circle is $360^{\circ}$.

The central angle subtended by the arc which is $1/12$ of the circle is:

$\frac{1}{12} \cdot 360^{\circ} = 30^{\circ}$

The peripheral angle is half of the central angle:

Peripheral Angle $= \frac{1}{2} \cdot \text{Central Angle}$

Peripheral Angle $= \frac{1}{2} \cdot 30^{\circ} = 15^{\circ}$

3. Final Answer

$15^{\circ}$