A reliable method
Mark corresponding vertices before using a scale factor. For a regular polygon, connect the exterior turning angle to a complete turn of 360 degrees.
The common trap
A length scale factor does not equal the area scale factor. An interior polygon angle is supplementary to its adjacent exterior angle.
Make the connection
Use a labeled sketch and test whether the enlarged result is physically larger. Diagrams need not be drawn to scale.
An exterior angle measures a turn
A regular hexagon has exterior angle 360/6=60 degrees and interior angle 180−60=120 degrees. The exterior angles describe one complete turn, while an interior-exterior pair forms a straight line. These two totals should not be mixed. If similar triangles have corresponding sides 2 and 6, the length factor is three. A second side of length five becomes fifteen, but an area of five becomes forty-five because area uses the factor squared. Mark corresponding sides first; a tidy but incorrectly paired ratio produces the wrong scaling.
Transfer, explain and check
A regular decagon has exterior angle 36 degrees and interior angle 144 degrees. Explain why the sum of its interior angles is 1440 degrees, whereas the sum of exterior turning angles remains 360 degrees.
What is each interior angle, in degrees, of a regular 6-sided polygon?
- The exterior turning angles total 360 degrees.
- Divide 360 by the number of equal angles.
- Subtract one exterior angle from 180 degrees.
Compare the other answer choices
Divide a straight angle by the side count.
Return the exterior rather than interior angle.
Use n−2 as the divisor for a full turn.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Cambridge IGCSE Mathematics 0580