Estimating angles

To estimate the size of an angle, try thinking in terms of counting in quarter turns, or right angles.

360° angle diagram

For example, the angle in the following diagram is acute - the line turns less than a right angle to get to the other line, so it must be between 0^\circ and 90^\circ.

Acute angle diagram

The angle in the following diagram is a reflex angle. The line turns through more than two right angles, but less than three right angles, so is between 180^\circ and 270^\circ.

Reflex angle diagram

To be even more accurate think in terms of 45^\circ angles.

360° angle diagram

This angle lies somewhere between 90^\circ and 135^\circ, but seems slightly closer to 135^\circ, so you could estimate that it is 120^\circ.

Estimating angles diagram