Radian measure- find angle POQ

This question is challenging me a little.
I believe I have the concept in mind.

Question:
Points P and Q lie on the circumference of a circle with centre O and radius 5cm. The difference between the areas of major sector POQ and minor sector POQ is 15cm². Find the angle POQ.

Firstly, we have two angles POQ. Can they not be more specific? I can assume that they mean the smallest angle.

I know that the area of a circle is A=πr² hence, 78.5cm² for this specific circle.

The difference of area is between the major and the minor sector. At first I thought minus the 15cm² from the circle but that would make the assumption that the full circle is a major sector meaning there’s no room for the minor sector. (This is just an example of my brain ruling out a possibility)

I don’t know if I need to introduce a formula I don’t know yet but I’m working with A=1/2r²theta(radians)

So, major + minor = 78.5cm²

Major-minor=15cm²

What am I missing here?

Thank you in advance

Nothing by the sounds of it. Its a classic
x + y = 25 pi
x - y = 15
problem with an easy solution? Then get the angle (proportion of the circle area) that corresponds to y.

In my head I’m thinking something along the lines of that but it’s not manifesting lol.

however, if I approach how I think is correct. Let y=minor and x=Major

X-Y=15
so, X=15+Y

I find 2y+15=25π.
Y=31.769 area for the minor sector

hence, 31.769=1/2(5)²(theta)
=2.54. Cool.

thank you for nudging my brain.

In my head I’m thinking something along the lines of that but it’s not manifesting lol.

however, if I approach how I think is correct. Let y=minor and x=Major

X-Y=15
so, X=15+Y

I find 2y+15=25π.
Y=31.769 area for the minor sector

hence, 31.769=1/2(5)²(theta)
=2.54. Cool.

thank you for nudging my brain.