Chapter 5: Understanding Quadrilaterals & Practical Geometry

Solution:-

(a) Opposite sides are parallel.

Solution:-

(c) 3

As we know that, obtuse angle is an angle between 90^o to 180^o.

The sum of the interior angles of a quadrilateral is equal to 360o. So all the angles can’t be obtuse since then the sum will more than 3600. Therefore a maximum of 3 obtuse angles that a quadrilateral have.

Solution:-

(b) n – 2

Solution:-

(c) 540^o

We know that, the sum of all the angles of a polygon is (n – 2) × 180^o.

Where ‘n’ is the number of sides in the polygon,

Then, pentagon has 5 sides, i.e. n = 5

So, (n – 2) × 180^o

(5 – 2) × 180^o

3 × 180^o

540^o

Solution:-

(d) 720^o

We know that, the sum of all the angles of a polygon is (n – 2) × 180^o.

Where ‘n’ is the number of sides in the polygon,

Then, hexagon has 6 sides, i.e. n = 6

So, (n – 2) × 180^o

(6 – 2) × 180^o

4 × 180^o

720^o

Solution:-

(a) 1: 3

Solution:-

(a) rhombus

A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a rhombus.

Solution:-

(a) rectangle

Solution:-

(a) Square

Solution:-

(a) 9

We know that,

The number of diagonals in a polygon of n sides is n(n – 3)/2

Where n = 6

Then,

= 6 × (6 – 3)/2

= 6 × 3/2

= 18/2

= 9