(i) 15 sides
(1) 9 sides
Find the measure of each exterior angle of a regular polygon
How many sides does a regular polygon have if the measure
How many sides does a regular polygon have if each
(a) Is it possible to have a regular polygon with measure of eache
(a)
(b) Can it be an interior angle of a regular polygon? Why?
a) What is the minimum interior angle possible for a regular
b) What is the maximum exterior angle possible for a regula
Kinds of Quadrilaterals
is 165°2
Answers
Answer:
Solution: We know that sum of exterior angles of a polygon = 360⁰
So,
125
°
+
125
°
+
x
=
360
°
Or,
250
°
+
x
=
360
°
Or,
x
=
360
°
=
250
°
=
110
°
Class 8 math Quadrilaterals exercise 3.1-2
Solution:
Class 8 math Quadrilaterals exercise 3.1-3
We know that sum of exterior angles of a polygon = 360⁰
So,
70
°
+
x
+
90
°
+
60
°
+
90
°
=
360
°
Or,
310
°
+
x
=
360
°
Or,
x
=
360
°
−
310
°
=
50
°
Question 2: Find the measure of each exterior angle of a regular polygon of
(i) 9 sides
Solution: Since, 9 sides of a polygon has nine angles
And we know that sum of exterior angles of a polygon = 360⁰
So, 9 exterior angles = 360°
Or, 1 exterior angle
=
360
°
÷
9
=
40
°
(ii) 15 sides
Solution: Since, 15 sides of a polygon has 15 angles
And we know that sum of exterior angles of a polygon = 360⁰
So, 15 exterior angles = 360°
Or, 1 exterior angle
=
360
°
÷
15
=
24
°
Question 3: How many sides does a regular polygon have if the measure of an exterior angle is 24⁰?
Solution:We know that number of angles of a polygon = number of sides
And we know that sum of exterior angles of a polygon = 360⁰
So, measure of each angle = 24°
Or, number of exterior angles
=
360
°
÷
24
°
=
15
Hence, number of sides = 15
Question 4: How many sides does a regular polygon have if each of its interior angles is 165⁰?
Solution: Here, each interior angle = 165°
Hence, each exterior angle = 180° - 165° = 15°
As, measure of each exterior angle = 15°
So, number of sides
=
360
°
÷
15
°
=
24
Hence, number of sides = 24
Question 5: (a) Is it possible to have regular polygon with measure of each exterior angle as 22⁰?