Constructing Angles

Section 1What angle construction means

Constructing an angle means drawing it accurately, usually from a given line and point. You may use a protractor, compass, ruler, and set squares depending on the instruction. Watch out: if the question says construct, do not just sketch by eye.

Section 2Basic angles

A 60 degree angle can be made with compass arcs from an equilateral triangle construction. A 30 degree angle can be made by bisecting 60 degrees. A 45 degree angle can be made by bisecting 90 degrees.

Section 3Combined angles

A 120 degree angle can be made by constructing two 60 degree angles or by using the outside angle from 60 degrees. A 75 degree angle is halfway between 60 and 90 degrees. A 105 degree angle is halfway between 90 and 120 degrees.

Section 4The 112 degree note

The roadmap says 112 degree angles. Here's the trick: use a protractor for an exact 112 degree angle unless your teacher gives a special construction method. If class notes say 112.5 degrees instead, that can be made by bisecting between 105 and 120 degrees.