Intermediate Problems 14 Isopolygons An isopolygon is a polygon in which each iterior angle is 60°, 120°, 240°, or 300°. For example, an equilateral triangle is an isopolygon as it rtangle is not an isopolygon as it contains Cont

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9.
Intermediate Problems
14 Isopolygons
An isopolygon is a polygon in which each interior angle is 60°, 120°,
240°, or 300°. For example, an equilateral triangle is an isopolygon as it
contains only 60° angles. A rectangle is not an isopolygon as it contains
90° angles.
Isopolygons can be conveniently drawn on an isometric grid. For ex-
ample, the diagram below shows an isoheptagon (a 7-sided isopolygon),
with four 60° angles, one 240 angle, one 120° angle and one 300° angle.
a Draw an isononagon (a 9-sided isopolygon) that has six 60° angles
and three 300° angles.
b Draw two different isopolygons each with four 240° angles and all
other angles 120°. (Two isopolygons are different if one is not a rota-
tion, reflection, magnification, or elongation of the other.)
c If an isopolygon has four 240° angles and all its other angles are 120°,
determine how many sides it has.
d An isopolygon has five 60° angles and two 300° angles. Show that
the number of 120° angles must be the same as the number of 240°
angles.
Transcribed Image Text:9. Intermediate Problems 14 Isopolygons An isopolygon is a polygon in which each interior angle is 60°, 120°, 240°, or 300°. For example, an equilateral triangle is an isopolygon as it contains only 60° angles. A rectangle is not an isopolygon as it contains 90° angles. Isopolygons can be conveniently drawn on an isometric grid. For ex- ample, the diagram below shows an isoheptagon (a 7-sided isopolygon), with four 60° angles, one 240 angle, one 120° angle and one 300° angle. a Draw an isononagon (a 9-sided isopolygon) that has six 60° angles and three 300° angles. b Draw two different isopolygons each with four 240° angles and all other angles 120°. (Two isopolygons are different if one is not a rota- tion, reflection, magnification, or elongation of the other.) c If an isopolygon has four 240° angles and all its other angles are 120°, determine how many sides it has. d An isopolygon has five 60° angles and two 300° angles. Show that the number of 120° angles must be the same as the number of 240° angles.
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