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P, Q and R lie on a circle, centre O.
Angle PQR = y° and angle POR = (2y-60)°.
Find the value of y.
pq and R line on a circle Center o angle pqr is equal to y° and angle p o r is equal to 2y - 60° find the value of y ​



Answer :

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.