Plane Angle

The plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius. The secondary SI unit for the plane angle is the radian.

The inclination of one line to another. One complete revolution equals 360° (degrees) or 2π radians.

1 degree (°)=π/180 radian1 radian (rad)=57.2958 degree (°)
1 minute (′)=1/60 degree (°)1 second (“)=1/60 minute (′)
1 grad (or grade)=1/100 right angleright angle=π/2 radian (rad)
Angle Conversions

The size of an object in the sky can be measured by the angle that it covers when viewed from Earth. The diameter of the full Moon is about one-half of a degree or 30 arcmin.

Coterminal Angles

An angle starts at the initial side and ends at the terminal side:

  • if this is anti-clockwise then the angle is positive
  • if this is clockwise then the angle is negative

Acute Angle – a positive angle that is less than 90 degrees.

Angle Bisector – a ray that divides an angle into two congruent angles.

Congruent Angles – two angles that are exactly the same.

corresponding angles

Corresponding Angles

Two angles in the same relative position on two lines when those lines are cut by a transversal.

Equality of corresponding angles:

A = E, C = G, B = F, D = H

Flat – an informal unit of angle measure equal to 1/6 turn or 60°. This comes from the fact that hexagonal nuts have 6 flat sides; to turn the nut one flat is to turn it 1/6 revolution.

Obtuse Angle – an angle larger than 90° but smaller than 180°.

incra protractor


A tool used to measure angles.

An Incra protractor has thin slots cut in the metal sheet that allow you to accurately mark angles.

Reflex Angle – an angle between 180° and 360°.

Right Angle – the angle formed when two straight lines intersect and the 4 angles at their crossing are all equal. Right angle = 90° = π/2 radians

Rise Run – for smaller angles, the ratio obtained when the change in offset between two centre lines is divided by the distance along either centerline. In effect, it is the slope of one line in a plane compared to another line in the same plane. Angularity is normally specified in mils/inch, or milliradians which is rise/run.

Straight Angle – an angle whose measure is 180 degrees.

Supplementary Angles – two angles are supplementary if they add up to 180°.

Terminal Side – the side that the measurement of an angle ends at.

Vertical Angles – two angles that share a common vertex and whose sides form 2 lines.

Zero Angle – an angle whose measure is 0. In a zero angle, both the initial and terminal sides are the same.

Wixey Digital Angle Gauge

How Good is Your Mobile Phone as an Angle Gauge?

I wanted to know how good is your Mobile Phone as an Angle Gauge? So I checked it against a known set of angles and a known gauge. So I set up an experiment using a surface table (an accurate flat plate), a sine bar and a Wixey angle gauge. 

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