Chapter 5: Understanding Quadrilaterals & Practical Geometry

Solution:-

The number of sides of a regular polygon, where each exterior angle has a measure of 36^o, is 10.

We know that, the measure of each exterior angle of a regular polygon is 360^o/n.

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

Then, exterior angle has a measure of 36^o

So, 36^o = 360^o/n

n = 360^o/36^o

n = 10

Solution:-

Concave polygon.

Concave polygon has more than one reflex angle.

Solution:-

A quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure is kite.

Solution:-

The measure of each angle of a regular pentagon is 108.

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

Measure of each angle = 540^o/5 = 108^o

Solution:-

The name of three-sided regular polygon is an equilateral triangle.

Solution:-

The number of diagonals in a hexagon is 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

Solution:-

A polygon is a simple closed curve made up of only line segments.

Solution:-

A regular polygon is a polygon whose all sides are equal and all angles are equal.

Solution:-

The sum of interior angles of a polygon of n sides is 2n – 4 right angles.

Solution:-

The sum of all exterior angles of a polygon is 360^o.