Answer:
Okay, let's work through this geometry problem step-by-step:
1. We are given that P, Q, and R lie on a circle with center O.
2. The angle PQR is equal to y degrees.
3. The angle POR is equal to 2y - 60 degrees.
4. We need to find the value of y.
To solve this, we can use the fact that inscribed angles on a circle are half the measure of the corresponding central angles.
* The inscribed angle PQR is y degrees.
* The corresponding central angle POQ is 2y degrees.
* The inscribed angle POR is 2y - 60 degrees.
* The corresponding central angle POQ is 4y - 120 degrees.
Since the central angles add up to 360 degrees, we can set up an equation:
2y + (4y - 120) = 360
Simplifying:
6y - 120 = 360
6y = 480
y = 80
Therefore, the value of y is 80 degrees.