Here are a couple hints to get you started.
You need to find the area of the purple. Then use the formula for the area of a sector (which requires the measure of the central angle (let's call that x) and set it equal to the area of the purple triangle.
How can you find the area of the triangle? One way is to recall that when you know two sides and an included angle the formula is A = 1/2(ab) sin C. In our case a and b are both 12 and C=30.
How do you find the area of the sector (pink)? Well the sector is a fraction of the area of the circle. As a matter of fact it is x/360 of the area of the circle. The circle has radius 12, so area of circle is 144pi.
So your equation so solve for x looks something like this: x/360 (144pi) = area found in part 1.Set it up and solve for x.