Constructing an angle can be a challenging concept for some students to learn, but once the process has been practiced using handson materials such as a ruler, protractor and compass, the steps may seem less complicated. Master the construction of simple angle measurements such as 60degree angles and 90degree angles before moving on to other angles or the bisection of angles. Always doublecheck your angle construction using a protractor and troubleshoot the process if the angle measurement is incorrect.
Things You'll Need
 Protractor
 Pencil
 Paper
 Compass
60Degree Angle

Draw a line segment using the straight edge of a protractor with a pencil. Open the compass to any width and place the point on one end of the line segment.

Draw an arc through the line segment and above the line segment to create 1/4 of a circle. Do not adjust the width of the compass and reposition the compass point to the intersection of the drawn arc and the line segment.

Draw a short arc with the compass to intersect the first arc. Connect the twoarced intersection with the starting point on the line segment, using the straight edge of the protractor.

Measure the 60degree angle with your protractor to doublecheck your work.
90Degree Angle

Draw a line segment on the paper using a pencil and the straight edge of the protractor. Open the compass so when the point is placed on one line segment end, the pencil touches the other end.

Draw a small arc over the estimated center of the line segment and another small arc underneath the estimated center of the line segment.

Reposition the compass so the point is on the opposite end of the line segment, without adjusting the width of the compass, and intersect both the arc above and below the line segment.

Lay the straight edge of the protractor as to connect the two intersecting arc points but only draw one line from the top intersection to the original line segment. This should create a 90degree angle.

Doublecheck the measurement with your protractor to ensure that it is 90 degrees.
References
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