1. Polygons Description Acute angle a triangle with two obtuse angles?
[ GM1.2 Support Plenary]
Is it possible to draw:
a triangle with two obtuse angles?
a quadrilateral with an obtuse and a reflex angle as two of its internal angles?
a pentagon with two reflex angles?
a regular polygon with external angles of 45°?
a regular polygon with external angles of 35°?
a hexagon with four acute angles?
a regular polygon with internal angles of 110°?
Type of angle
Description
Acute angle
An angle less than
90°
Right angle
An angle that is exactly 90°
Obtuse angle
An angle that is greater than 90° but less than 180°
Reflex angle
An angle that is greater than 180°
Preamble
These questions are useful for pairs or small groups to encourage experimentation and discussion.
Possible content
Using the language of angles and polygons and the simple angle properties of the latter. Recognising acute, obtuse and reflex angles.
Resources
None but perhaps some protractors in order to resolve disputes.
Solution/Notes
Impossible: angle sum of triangle is 180°
Possible: for example an arrowhead
Possible: any pentagon resembling a three pointed star
Possible: (360 ÷ 45 = 8)
Impossible: (360 ÷ 35 not a whole number (of sides))
Possible: (hexagon resembling a bow tie)
Impossible: (110 does not fit the internal angle formula; or 360 ÷ (180 – 110) is not a whole number.)
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010