Selina solutions for Concise Mathematics [English] Class 8 ICSE chapter 16 - Understanding Shapes [Latest edition]

State which of the following are polygons :

(i)

(ii) 

(iii)  

(iv)

(v)

(vi)

If the given figure is a polygon, name it as convex or concave.

Calculate the sum of angle of a polygon with: 10 sides

Calculate the sum of angle of a polygon with: 12 sides

Calculate the sum of angle of a polygon with: 20 sides

Calculate the sum of angle of a polygon with : 25 sides

Find the number of sides in a polygon if the sum of its interior angle is: 900°

Find the number of sides in a polygon if the sum of its interior angle is: 1620°

Find the number of sides in a polygon if the sum of its interior angle is: 16 right-angles.

Find the number of sides in a polygon if the sum of its interior angle is: 32 right-angles.

Is it possible to have a polygon, whose sum of interior angle is: 870°

Is it possible to have a polygon, whose sum of interior angle is: 2340°

Is it possible to have a polygon, whose sum of interior angle is: 7 right-angles

Is it possible to have a polygon, whose sum of interior angle is:  4500°

If all the angles of a hexagon are equal, find the measure of each angle.

If all the angles of a 14-sided figure are equal ; find the measure of each angle.

Find the sum of exterior angle obtained on producing, in order, the side of a polygon with: 7 sides

Find the sum of exterior angle obtained on producing, in order, the side of a polygon with : 10 sides

Find the sum of exterior angle obtained on producing, in order, the side of a polygon with: 250 sides

The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x – 1)°, (10x + 2)°, (8x + 2)° (9x – 3)°, (5x + 4)° and (12x + 6)° ; find each exterior angle.

The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.

Two angles of a hexagon are 120° and 160°. If the remaining four angles are equal, find each equal angle.

The figure, given below, shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B : ∠C : ∠D = 5: 6: 7.

(i) Using the formula, find the sum of the interior angles of the pentagon.

(ii) Write the value of ∠A + ∠E

(iii) Find angles B, C and D.

Two angles of a polygon are right angles and the remaining are 120° each. Find the number of sides in it.

In a hexagon ABCDEF, side AB is parallel to side FE and ∠B : ∠C : ∠D : ∠E = 6 : 4 : 2 : 3. Find ∠B and ∠D.

The angles of a hexagon are x + 10°, 2x + 20°, 2x – 20°, 3x – 50°, x + 40° and x + 20°. Find x.

In a pentagon, two angles are 40° and 60°, and the rest are in the ratio 1 : 3 : 7. Find the biggest angle of the pentagon.

Fill in the blanks :
In case of regular polygon, with :

Find the number of sides in a regular polygon, if its interior angle is: 160°

Find the number of sides in a regular polygon, if its interior angle is: 135°

Find the number of sides in a regular polygon, if its interior angle is: `1 1/5` of a right angle

Find the number of sides in a regular polygon, if its exterior angle is : `1/3` of right angle

Find the number of sides in a regular polygon, if its exterior angle is: two-fifth of right angle

Is it possible to have a regular polygon whose interior angle is : 170°

Is it possible to have a regular polygon whose interior angle is:

138°

Is it possible to have a regular polygon whose each exterior angle is: 80°

Is it possible to have a regular polygon whose each exterior angle is: 40° of a right angle.

Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.

The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :

(i) measure of each interior angle ;
(ii) measure of each exterior angle and
(iii) number of sides in the polygon.

The ratio between the interior angle and the exterior angle of a regular polygon is 2: 1. Find:

(i) each exterior angle of the polygon ;
(ii) number of sides in the polygon.

The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.

The sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of the polygon.

AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = 20° ; find :

(i) its each interior angle,
(ii) its each exterior angle
(iii) the number of sides in the polygon.

Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.

In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:

(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED

The difference between the exterior angles of two regular polygons, having the sides equal to (n – 1) and (n + 1) is 9°. Find the value of n.

If the difference between the exterior angle of a 'n' sided regular polygon and an (n + 1) sided regular polygon is 12°, find the value of n.

The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.

Three of the exterior angles of a hexagon are 40°, 51 ° and 86°. If each of the remaining exterior angles is x°, find the value of x.

Calculate the number of sides of a regular polygon, if:  its interior angle is five times its exterior angle.

Calculate the number of sides of a regular polygon, if: the ratio between its exterior angle and interior angle is 2: 7.

Calculate the number of sides of a regular polygon, if: its exterior angle exceeds its interior angle by 60°.

The sum of interior angles of a regular polygon is thrice the sum of its exterior angles. Find the number of sides in the polygon.

Two angles of a quadrilateral are 89° and 113°. If the other two angles are equal; find the equal angles.

Two angles of a quadrilateral are 68° and 76°. If the other two angles are in the ratio 5 : 7; find the measure of each of them.

Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x – 20)° and 6(x+3)°. Find :

(i) the value of x.
(ii) each angle of the quadrilateral.

Use the information given in the following figure to find :

(i) x
(ii) ∠B and ∠C

In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4 : 5

(i) Calculate each angle of the quadrilateral.

(ii) Assign a special name to quadrilateral ABCD

From the following figure find;

1. x
2. ∠ABC
3. ∠ACD

Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a+2)° and ∠B = 2(2a+7)°.
Calculate ∠A.

In the given figure : ∠b = 2a + 15 and ∠c = 3a + 5; find the values of b and c.

Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.

In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other
(i) Is PS also parallel to QR?
(ii) Assign a special name to quadrilateral PQRS.

Use the information given in the following figure to find the value of x.

The following figure shows a quadrilateral in which sides AB and DC are parallel. If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.

Use the following figure to find the value of x

ABCDE is a regular pentagon. The bisector of angle A of the pentagon meets the side CD in point M. Show that ∠AMC = 90°.

In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively. Show that:

∠AOB = (∠C + ∠D)