8th Maths 3.2
NCERT Class 8th solution of Exercise 3.1
NCERT Class 8th solution of Exercise 3.3
NCERT Class 8th solution of Exercise 3.4
Exercise 3.2
Q1. Find the following figures.
a)
`text{Sol.}`
`text{We know that}`
`text{Sum of the external angles of a polygon is }360^circ.`
`text{x }+125^circ+125^circ = 360^circ`
`text{x} = 360^circ - 250^circ`
`text{x} = 110^circ`
`text{Answer:}`
`text{x} = 110^circ`.
b)
`text{Sol.}`
`text{We know that}`
`text{Sum of the external angles of a polygon is }360^circ.`
`text{x }+90^circ+60^circ+90^circ+70^circ = 360^circ`
`text{x} = 360^circ - 310^circ`
`text{x} = 50^circ`
`text{Answer:}`
`text{x} = 50^circ`
Q2. Find the measure of each exterior angle of a regular polygon of
i) `text{9 sides}`
`text{Sol.}`
`text{exterior angle} =(text{Total of all exterior angles})/(text{Total no. of sides})`
`= 360^circ/9`
`= 40^circ`
`text{Answer:}`
`40^circ.`
ii) `text{15 sides}`
`text{Sol.}`
`text{exterior angle} =(text{Total of all exterior angles})/(text{Total no. of sides})`
`= 360^circ/15`
`= 24^circ`
`text{Answer:}`
`24^circ`.
Q3. How many sides does a regular polygon have if the measure of an exterior angle is `24^circ`?
`text{Sol.}`
`text{No. of sides} = text{(Total of all exterior angles)}/text{a exterior angle}`
`= 360^circ/24^circ`
`= 15`
`text{Answer:}`
`15.`
Q4. How many sides does a regular polygon have if each of its interior angles is `165^circ`?
`text{Sol.}`
`text{measure of a interior angle }= ((text{n}-2)180^circ)/text{n}`
`text{where n = no of sides}`
`165^circ = ((text{n}-2)180^circ)/text{n}`
`165^circtext{n} = 180^circ text{n} - 360^circ`
`180^circtext{n}-165^circ = 360^circ`
`15^circ text{n} = 360^circ`
`text{n} = 360^circ/15^circ`
`text{n} = 24`
`text{Answer:}`
`text{Number of sides 24}`.
Q5.
a) Is it possible to have a regular polygon with measure of each exterior angle as `22^circ`?
`text{Answer:}`
`text{No, because 22 is not a divisor of 360.}`
b) Can it be an interior angle of a regular polygon? Why?
`text{Answer:}`
`text{No, because each exterior angle is } 180^circ - 22^circ`
` = 158^circ text{which is not a divisor of }360^circ`.
Q6.
a) What is the minimum interior angle possible for a regular polygon? Why?
`text{Answer:}`
`text{The equilateral triangle being a regular polygon}`
`text{of 3 sides has the least measure of an interior}`
`text{angle =}60^circ`.
b) What is the maximum exterior angle possible for a regular polygon?
`text{Answer:}`
`text{By (a), we can see that the greatest exterior}`
`text{angle is }120^circ.`
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