# Rectilinear Figures Class-9th Concise Selina ICSE Maths Solutions

**Rectilinear Figures Class-9th Concise** Selina ICSE Maths Solutions Chapter-14. We provide step by step Solutions of Exercise / lesson-14 **Rectilinear Figures (**Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium) ** **for ICSE **Class-9th Concise** Selina Mathematics by R K Bansal.

Our Solutions contain all type Questions with Exe-14 A, Exe-14 B, and Exe-14 C, to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-9th Mathematics .

## Rectilinear Figures Class-9th Concise Selina ICSE Maths Solutions Chapter-14 **(**Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium)

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**Exercise – 14 A, Rectilinear Figures Class-9th Concise**** ****(**Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium)

Question 1

The sum of the inteior angles of a polygon is four times the sum of its exterior angles. Find the number of sides in the polygon.

Answer

The sum of the interior angle=4 times the sum of the exterior angles.

Therefore the sum of the interior angles = 4×360° =1440°.

Now we have

Thus the number of sides in the polygon is 10.

#### Question 2

The angles of a pentagon are in the ratio 4 : 8 : 6 : 4 : 5. Find each angle of the pentagon.

Answer

Let the angles of the pentagon are 4x, 8x, 6x, 4x and 5x.

Thus we can write

#### Question 3

One angle of a six-sided polygon is 140^{o} and the other angles are equal. Find the measure of each equal angle.

Answer

Let the measure of each equal angles are x.

Then we can write

Therefore the measure of each equal angles are 116 ‘

#### Question 4

In a polygon there are 5 right angles and the remaining angles are equal to 195^{o} each. Find the number of sides in the polygon.

Answer

Let the number of sides of the polygon is *n* and there are k angles with measure 195^{o}.

Therefore we can write:

In this linear equation n and k must be integer. Therefore to satisfy this equation the minimum value of k must be 6 to get n as integer.

Hence the number of sides are: 5 + 6 = 11.

#### Question 5

Three angles of a seven sided polygon are 132^{o} each and the remaining four angles are equal. Find the value of each equal angle.

Answer

Let the measure of each equal angles are x.

Then we can write:

Thus the measure of each equal angles are 126o.

#### Question 6

Two angles of an eight sided polygon are 142^{o} and 176^{o}. If the remaining angles are equal to each other; find the magnitude of each of the equal angles.

Answer

Let the measure of each equal sides of the polygon is x.

Then we can write:

Thus the measure of each equal angles are 127^{o}.

#### Question 7

In a pentagon ABCDE, AB is parallel to DC and ∠A : ∠E : ∠D = 3 : 4 : 5. Find angle E.

Answer

Let the measure of the angles are 3x, 4x and 5x.

Thus

Thus the measure of angle E will be 4×30=120

#### Question 8

AB, BC and CD are the three consecutive sides of a regular polygon. If BAC = 15^{o}; find,

(i) Each interior angle of the polygon.

(ii) Each exterior angle of the polygon.

(iii) Number of sides of the polygon

Answer

(i)

Let each angle of measure x degree.

Therefore measure of each angle will be:

Thus the number of sides are 12.

#### Question 9

The ratio between an exterior angle and an interior angle of a regular polygon is 2 : 3. Find the number of sides in the polygon.

Answer

Let measure of each interior and exterior angles are 3k and 2k.

Let number of sides of the polygon is n.

Now we can write:

Thus the number of sides of the polygon is 5.

#### Question 10

The difference between an exterior angle of (n – 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6^{o} find the value of n.

Answer

For (n-1) sided regular polygon:

Let measure of each angle is x.

Therefore

Thus the value of n is 13.

#### Question 11

Two alternate sides of a regular polygon, when produced, meet at right angle. Find:

(i) The value of each exterior angle of the polygon;

(ii) The number of sides in the polygon.

Answer

(i)

Let the measure of each exterior angle is x and the number of sides is n.

Therefore we can write:

require number of side of regular polygon = 8

**Concise** Selina Solutions for ICSE Class-9 Maths **Exercise – 14 B** **Rectilinear Figures ****(**Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium)

Question 1

State, ‘true’ or ‘false’

(i) The diagonals of a rectangle bisect each other.

(ii) The diagonals of a quadrilateral bisect each other.

(iii) The diagonals of a parallelogram bisect each other at right angle.

(iv) Each diagonal of a rhombus bisects it.

(v) The quadrilateral, whose four sides are equal, is a square.

(vi) Every rhombus is a parallelogram.

(vii) Every parallelogram is a rhombus.

(viii) Diagonals of a rhombus are equal.

(ix) If two adjacent sides of a parallelogram are equal, it is a rhombus.

(x) If the diagonals of a quadrilateral bisect each other at right angle, the quadrilateral is a square.

Answer

(i)True.

This is true, because we know that a rectangle is a parallelogram. So, all the properties of a parallelogram are true for a rectangle. Since the diagonals of a parallelogram bisect each other, the same holds true for a rectangle.

(ii)False

This is not true for any random quadrilateral. Observe the quadrilateral shown below.

Clearly the diagonals of the given quadrilateral do not bisect each other. However, if the quadrilateral was a special quadrilateral like a parallelogram, this would hold true.

(iii)False

Consider a rectangle as shown below.

It is a parallelogram. However, the diagonals of a rectangle do not intersect at right angles, even though they bisect each other.

(iv)True

Since a rhombus is a parallelogram, and we know that the diagonals of a parallelogram bisect each other, hence the diagonals of a rhombus too, bisect other.

(v)False

This need not be true, since if the angles of the quadrilateral are not right angles, the quadrilateral would be a rhombus rather than a square.

(vi)True

A parallelogram is a quadrilateral with opposite sides parallel and equal.

Since opposite sides of a rhombus are parallel, and all the sides of the rhombus are equal, a rhombus is a parallelogram.

(vii)False

This is false, since a parallelogram in general does not have all its sides equal. Only opposite sides of a parallelogram are equal. However, a rhombus has all its sides equal. So, every parallelogram cannot be a rhombus, except those parallelograms that have all equal sides.

(viii)False

This is a property of a rhombus. The diagonals of a rhombus need not be equal.

(ix)True

A parallelogram is a quadrilateral with opposite sides parallel and equal.

A rhombus is a quadrilateral with opposite sides parallel, and all sides equal.

If in a parallelogram the adjacent sides are equal, it means all the sides of the parallelogram are equal, thus forming a rhombus.

(x)False

Observe the above figure. The diagonals of the quadrilateral shown above bisect each other at right angles, however the quadrilateral need not be a square, since the angles of the quadrilateral are clearly not right angles.

Question 2

In the figure, given below, AM bisects angle A and DM bisects angle D of parallelogram ABCD. Prove that : AMD = 90^{o.}

^{…………………}

Answer

From the given figure we conclude that

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