NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1.
- Understanding Quadrilaterals Class 8 Ex 3.2
- Understanding Quadrilaterals Class 8 Ex 3.3
- Understanding Quadrilaterals Class 8 Ex 3.4
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 8 |
| Subject | Maths |
| Chapter | Chapter 3 |
| Chapter Name | Understanding Quadrilaterals |
| Exercise | Ex 3.1 |
| Number of Questions Solved | 7 |
| Category | NCERT Solutions |
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1
Ex 3.1 Class 8 Maths Question 1.
Given here are some figures :
Classify each of them on the basis of the following :
(a) Simple curve
(b) Simple closed curve
(c) Polygon
(d) Convex polygon
(e) Concave polygon
Solution.
The classification of the given figures is as under :
(a) Simple curve : (1), (2), (5), (6), (7) and (8)
(b) Simple closed curve : (1), (2), (5), (6) and (7)
(c) Polygon: (1) and (2)
(d) Convex polygon : (2)
(e) Concave polygon : (1) and (4)
Ex 3.1 Class 8 Maths Question 2.
How many diagonals does each of the following have?
(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle.
Solution.
(a) A convex quadrilateral has two diagonals.
(b) A regular hexagon has nine diagonals.
(c) A triangle has no diagonal.
Ex 3.1 Class 8 Maths Question 3.
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 j try!)
Solution.
The sum of measures of the angles of a convex quadrilateral is 360°. Yes, this property holds in case of the quadrilateral is not convex.
Ex 3.1 Class 8 Maths Question 4.
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) n
Solution.
From the given table, dearly we observe that the sum of angles (interior angles) of a polygon with n sides = (n – 2) x 180°.
(a) n = 7
∴ The sum of the angles of a polygon of 7 sides
Angle sum =
=
(b) n = 8
∴ The sum of the angles of a polygon of 8 sides
Angle sum =
=
(c) n = 10
∴ The sum of the angles of a polygon of 10 sides
Angle sum =
=
(d) Clearly from the given table it is observed that the number of triangles is two less them the number of sides in the polygon.
∴ If the polygon has n sides, the number of triangles formed will be (n – 2).
Since the sum of angles of a triangle = 180°
∴ The sum of angles of a polygon of n sides = (n – 2) x 180°.
Ex 3.1 Class 8 Maths Question 5.
What is a regular polygon? State the name of a regular polygon of
(i) 3 slides
(ii) 4 slides
(iii) 6 slides
Solution.
A polygon is said to be a regular polygon, if all its
- interior angles are equal;
- sides are equal; and
- exterior angles are euqal.
The name of a regular polygon of
- 3 sides is equilateral triangle.
- 4 sides is square.
- 6 sides is regular hexagon.
Ex 3.1 Class 8 Maths Question 6.
Find the angle measure x in the following figures.
Solution.
Ex 3.1 Class 8 Maths Question 7.
(a) Find x + y + z
(b) Find x + y + z + w.
Solution.
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