2. Find the number of sides of a polygon if
the sum of the interior angles is
a) 10 right angles b) 720°
d) 540°
c) 1620°
c) 9 sides
d) 18 sides
5. Find the number of sides of a regular
polygon if each interior angle is
a) 144°
b) 160°
c) 156°
d) 120°
3. Find the measure of each interior angle of
the following regular polygon.
b) Decagon
d) Hexagon
a) Nonagon
c) 24-gon
6. Is it possible to have a regular polygon
with an exterior angle of measure 25°?
4. Find the measure of each exterior angle of
a regular polygon having
b) 30 sides
7. Find the sum of the interior angles of a
polygon having
a) 7 sides
b) 11 sides c) 16 sides
a) 12 sides
Answers
Step-by-step explanation:
2.Since the figure with angles measuring 0˚ is 1 line, then the figure with interior angles of 720˚ has 1+5=6 sides.
5.We will substitute the given values of angles to find the number of corresponding sides. Therefore, a regular polygon with an interior angle of 90∘will have 4 sides. Therefore, a regular polygon with an interior angle of 108∘will have 5 sides.
3. To find the value of the interior angle of a regular polygon, the equation is (n−2)180∘n where n is the number of sides of the regular polygon.
6.No
4.The measure of each exterior angle of a regular polygon is given by; The measure of each exterior angle =360°/n, where n = number of sides of a polygon. One important property about a regular polygon's exterior angles is that the sum of the measures of the exterior angles of a polygon is always 360°.
7.We know that if a polygon has 'n' sides, then it is divided into (n – 2) triangles. We also know that, the sum of the angles of a triangle = 180°. Therefore, the sum of interior angles of a polygon having n sides is (2n – 4) right angles. Thus, each interior angle of the polygon = (2n – 4)/n right angles.