☰
Understanding Quadrilaterals
Question 5. (a) Is it possible to have a regular polygon with measure of each exterior angle is 22°?
(b) Can it be an interior angle of a regular polygon? Why?
Which is not a whole number.
If it is a regular polygon, then its number of sides must be a whole number.
(b) If 22° is an interior angle, then 180° - 22°, i.e. 158° is exterior angle.
Thus, 22° cannot be an interior angle of a regular polygon.
Sponsor Area
What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that).
|
Figure |
|
|
|
|
|
Side |
3 |
4 |
5 |
6 |
|
Angle sum |
180° |
2 x 180° = (4 - 2) x 180° |
3 x 180° = (5 - 2) x 180° |
4 x 180° = (6 - 2) x 180° |
What can you say about the angle sum of a convex polygon with number of sides?
(a) 7 (b) 8 (c) 10 (d) n
What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides (ii) 4 sides (iii) 6 sides
Find the angle measure x in the following figures. 
Find x in the following figures.
Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
How many sides does a regular polygon have if each of its interior angles is 165°?
Question 5. (a) Is it possible to have a regular polygon with measure of each exterior angle is 22°?
(b) Can it be an interior angle of a regular polygon? Why?
Sponsor Area
Sponsor Area
