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 = \(\left( 7-2 \right) \times { 180 }^{ \circ }\)

= \(5\times { 180 }^{ \circ }={ 900 }^{ \circ }\)

**(b)** n = 8

∴ The sum of the angles of a polygon of 8 sides

Angle sum = \(\left( 8-2 \right) \times { 180 }^{ \circ }\)

= \(6\times { 180 }^{ \circ }={ 1080 }^{ \circ }\)

**(c)** n = 10

∴ The sum of the angles of a polygon of 10 sides

Angle sum = \(\left( 10-2 \right) \times { 180 }^{ \circ }\)

= \(8\times { 180 }^{ \circ }={ 1440 }^{ \circ }\)

**(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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