Question

Points P, Q and R lie on the circumference of a circle, centre O.

Angle PQR = 29º.

Not drawn

to scale

Work out the size of the reflex angle POR.

Answer 1

The reflex angle POR can be found by subtracting the given angle PQR from 360 degrees. Therefore, the reflex angle POR is 331 degrees.

Step-by-step explanation:

The reflex angle POR can be found by subtracting the given angle PQR from 360 degrees. Since a full circle is 360 degrees, the reflex angle will be the remaining angle after subtracting PQR.

Reflex angle POR = 360 degrees - Angle PQR = 360 degrees - 29 degrees = 331 degrees.

Answer 2

To find the reflex angle POR when angle PQR is 29º, you double the angle PQR to get the central angle POR (58º) and then subtract from 360º to find the reflex angle POR, which is 302º.

Step-by-step explanation:

The question involves finding the size of the reflex angle POR given that angle PQR is 29º in a circle with center O. A reflex angle is an angle that is greater than 180º but less than 360º. In a circle, the angle at the center (angle POR in this case) is twice the angle at the circumference (angle PQR) when the angles subtend the same arc. Therefore, angle POR is twice angle PQR.

1. Identify the given angle at the circumference, which is angle PQR = 29º.
2. Calculate the corresponding central angle, which is twice the circumference angle, so angle POR = 2 × 29º = 58º.
3. Since the reflex angle is the larger portion of the circle not covered by angle POR, subtract the central angle from 360º to find the reflex angle: Reflex angle POR = 360º - 58º = 302º.

The size of the reflex angle POR is 302º.