8th Maths 3.1
NCERT Class 8th solution of Exercise 3.2
NCERT Class 8th solution of Exercise 3.3
NCERT Class 8th solution of Exercise 3.4
NCERT Class 8th solution of Exercise 2.1
Exercise 3.1
Q1. Given here are some figures.
Classify each of them on the basis of the following.
a) Simple curved
b) Simple closed curved curve
c) Polygon
d) Convex polygon
e) Concave polygon
`text{Answer:}`
a) `1, 2, 5, 6, 7`
b) `1, 2, 5, 6, 7`
c) `1, 2`
d) `2`
e) `1`
Q2. How many diagonals does each of the following have?
a) A convex quadrilateral
b) A regular hexagon
c) A triangle
`text{Answer:}`
a) `2`, b) `9`, c) `0`
Q3. 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!)
`text{Answer:}`
`360^circ, text{ yes.}`
Q4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
What can you say about the angle sum of a convex polygon with number of sides?
a) `7`
b) `8`
c) `10`
d) `text{n}`
a)
`text{Sol.}`
`text{Number of sides 7}`
`text{Angle sum = (n - 2)}times180^circ`
`= (7 - 2)times 180^circ`
`= 5times180^circ`
`= 900^circ`
`text{Answer:}`
`900^circ`.
b)
`text{Sol.}`
`text{Number of sides 8}`
`text{Angle sum = (n - 2)}times180^circ`
`= (8 - 2)times 180^circ`
`= 6times180^circ`
`= 1080^circ`
`text{Answer:}`
`1080^circ.`
c)
`text{Sol.}`
`text{Number of sides 10}`
`text{Angle sum = (n - 2)}times180^circ`
`= (10 - 2)times 180^circ`
`= 8times180^circ`
`= 1440^circ`
`text{Answer:}`
`1440^circ.`
d)
`text{Sol.}`
`text{Number of sides n}`
`text{Angle sum = (n - 2)}times180^circ`
`text{Answer:}`
`text{(n - 2)}180^circ.`
Q5. What is a regular polygon?
State the name of a regular polygon of
i) `3 text{ sides}`
ii) `4 text{ sides}`
iii) `6 text{ sides}`
`text{Answer:}`
`text{A polygon with equal sides and equal angles.}`
i)
`text{Answer}`
`text{Equilateral triangle}`
ii)
`text{Answer}`
`text{Square.}`
iii)
`text{Answer}`
`text{Regular haxagon}`
Q6. Find the angle measure `text{x}` in the following figures.
`text{Sol.}`
`text{Number of sides 4}`
`text{Angle sum = (n - 2)}times180^circ`
`= (4 - 2)times 180^circ`
`= 2times180^circ`
`= 360^circ`
`text{x }+ 50^circ + 130^circ + 120^circ = 360^circ`
`text{x }= 360^circ - 300^circ`
`text{x }= 60^circ`
`text{Answer}`
`60^circ.`
b)
`text{Sol.}`
`text{Number of sides 4}`
`text{Angle sum = (n - 2)}times180^circ`
`= (4 - 2)}times 180^circ`
`= 2times180^circ`
`= 360^circ`
`text{x }+ 60^circ + 70^circ + 90^circ = 360^circ`
`text{x }= 360^circ - 220^circ`
`text{x }= 140^circ`
`text{Answer}`
`140^circ`
c)
`text{Sol.}`
`text{Number of sides 5}`
`text{Angle sum = (n - 2)}times180^circ`
`= (5 - 2)}times 180^circ`
`= 3times180^circ`
`= 540^circ`
`text{x + x }+ 30^circ + (180^circ - 70^circ) + (180^circ - 60^circ) = 540^circ`
`text{2x }+ 30^circ + 110^circ + 120^circ = 540^circ`
`text{2x }= 540^circ - 260^circ`
`text{x }= 280^circ/2`
`text{x }= 140^circ`
`text{Answer}`
`140^circ.`
d)
`text{Sol.}`
`text{Number of sides 5}`
`text{Angle sum = (n - 2)}times180^circ`
`= (5 - 2)}times 180^circ`
`= 3times180^circ`
`= 540^circ`
`text{x + x + x + x + x } = 540^circ`
`text{x }= 540^circ/5`
`text{x }= 108^circ`
`text{Answer}`
`108^circ.`
Q7.
a) Find `x + y + z`
`text{Sol.}`
`x + 90^circ = 180^circ__ text{[By linear pair]}`
`x = 180^circ - 90^circ`
`x = 90^circ`
`z + 30^circ = 180^circ__text{[By linear pair]}`
`z = 180^circ - 30^circ`
`z = 150^circ`
`y = (90^circ + 30^circ)__text{[By exterior angle]}`
`y = 120^circ`
`x + y + z = 90^circ + 150^circ + 120^circ`
`= 360^circ`
`text{Answer:}`
`360^circ`
b) Find `x + y + z + w`
`text{Sol.}`
`x + 120^circ = 180^circ text{[By linear pair]}`
`x = 180^circ - 120^circ`
`x = 60^circ`
`y + 80^circ = 180^circ __text{[By linear pair]}`
`y = 180^circ - 80^circ`
`y = 100^circ`
`z + 60^circ = 180^circ__ text{[By liner pair]}`
`z = 180^circ - 60^circ`
`z = 120^circ`
`text{By angle sum property of quadrilateral}`
`angle zwx = 360^circ - (120^circ + 80^circ + 60^circ)`
`angle zwx = 360^circ - 260^circ`
`angle zwx = 100^circ`
`w +100^circ =180^circ__ text{[by linear pair]}`
`w = 180^circ - 100^circ`
`w = 80^circ`
`x + y + z + w = 60^circ + 100^circ + 120^circ + 80^circ`
`= 360^circ`
`text{Answer:}`
`360^circ`.
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