Draw triangles, quadrilaterals, and regular polygons (5, 6, 8, or 10 sides) with given angle measures.

ricojakezander@gmail.com
Polygons

Learning Competency:
•Draw triangles, quadrilaterals, and
regular polygons (5, 6, 8, or 10
sides) with given angle measures.

PRE-ASSESSMENT

TRUE OR FALSE
1.A polygon is a closed figure made up of line
segments. (True/False)
2.A polygon can have curved sides. (True/False)
3.A polygon with three sides is called a triangle.
(True/False)
4.A polygon with four sides is called a
quadrilateral. (True/False)
5.A polygon with five sides is called a pentagon.
(True/False)

TRUE OR FALSE
6.A polygon with six sides is called a hexagon.
(True/False)
7.A polygon with seven sides is called a heptagon.
(True/False)
8.A polygon with eight sides is called an octagon.
(True/False)
9.A polygon with nine sides is called a nonagon.
(True/False)
10.A polygon with ten sides is called a decagon.
(True/False)

What are polygons?
◆ Polygons are closed
figures made up of line
segments (not curves).
◆ A minimum of three line
segments are required to
make up a polygon – a 3
sided polygon is called a
triangle

Polygons we see in real life
Pentagon House USA
Octagon – Road sign
Hexagon – Bee hive
Hexagon – pencil
Decagon – Coin
Septagon – medicine box

Classifying Polygons
◆ Based on number of sides
Triangle – 3 sides Octagon – 8 sides
Quadrilateral- 4 sides Nonagon – 9 sides
Pentagon – 5 sides Decagon – 10 sides
Hexagon-6 sides Undecagon – 11 sides
Hepta/Septagon – 7 sides Dodecagon- 12 sides

◆ Based on type of angles
• Concave – At least one of the interior angles is a
reflex angle i.e. more than 180
• Convex – None of the angles are greater than
180
Concave octagon octagon
Convex

Classifying Polygons
◆ Based on equality of sided
• Regular Polygons – All sides and interior angles
are equal
• Irregular polygons – All sides are not equal
Irregular
Hexagon
Regular
Hexagon

Number of diagonals in a polygon

Diagonal
◆ A line segment
joining 2 non
consecutive
vertices of a
polygon is called a
diagonal.

Angle facts about Polygons
◆ A polygon has as many interior
angles as the number of sides
◆ Sum of exterior angles of all
polygons (irrespective of the
number of sides is 360 degrees
◆ Sum of exterior angle and interior
angle is always 180 degrees
◆ In a Regular polygon all exterior
angles are equal and all interior
angles are also equal.

Interior angles of a Polygons
Number of sides – 12 (n)
Number of triangles formed (by joining
diagonals) – (n-2) - 10
Sum of all interior angles = sum of angles
of the triangles formed = 10 ×180 degrees
= 1800 degrees
Sum of interior angles of a polygon =
(n-2)180 degrees

Practice Questions - All
Fill in the blanks – In case of a regular polygon if:
No. of Sides Exterior Angle Interior Angle No. of
Diagonals
i. 8
ii. 12
iii. 72°
iv. 45°
v. 150°
vi. 140°
vii. 35

Performance task 1.2

Practice Questions
1. Find the measure of each exterior angle of a
regular
(i) Pentagon
(ii) Hexagon
(iii) Heptagon
(iv) Decagon
(v) Polygon of 15 sides.
2. Is it possible to have a regular polygon each of
whose exterior angles is 50°?

Practice Questions
3. Find the measure of each interior angle of a regular polygon
having
(i) 10 sides
(ii) 15 sides
4. Is it possible to have a regular polygon each of whose interior
angles is 100o?
5. Is it possible to have a regular polygon with each exterior
angle as 22? Can it be an interior angle of a regular polygon?
6. What is the minimum interior angle possible for a regular
polygon? What is the maximum exterior angle possible for a
regular polygon?

Practice Questions
Select the correct answer in each of the following:
1. How many diagonals are there in
pentagon?
(a) 5
(b) 7
(c) 6
(d) 10

2. How many diagonals are
there in a hexagon?
(a) 6
(b) 8
(c) 9
(d) 10

3. How many diagonals are
there in an octagon?
(a) 8
(b) 16
(c) 18

4. How many diagonals are there
in a polygon having 12 sides?
(a)12
(b) 24
(c) 36
(d) 54

5. A polygon has 27 diagonals. How
many sides does it have?
(a) 7
(b) 8
(c) 9
(d) 12

6. The angles of a pentagon are ,
(x+20)o,(x+40)o, (x+60)o and (x+80)o.
The smallest angle of the pentagon is
(a)
(b)
(c)
(d)
𝒙°
7 𝟓 °
6 𝟖 °
7 𝟖 °
8 𝟓 °

7. The measurement of each exterior
angle of a regular polygon is .
How many sides does it have?
(a) 8
(b) 9
(c) 6
(d) 10
4 𝟎 °

Practice Questions
◆ Find x in the following figures
◆ Find the measure of each exterior angle of a regular
polygon of
(i) 9 sides
(ii) 15 sides

Practice Questions
◆ How many sides does a regular
polygon have if the measure of an
exterior angle is 24°?
◆ How many sides does a regular
polygon have if each of its interior
angles is 165°?

Questions

Practice sums - All
1. Calculate the sum of angles of a polygon with
a) 10 sides b) 12 sides c) 20 sides
2. Calculate the number of sides of a polygon , if the sum of its interior
angles is:
a) 900° b) 1620° c)16 right angles
3. Is it possible to have a polygon whose sum of interior angles is
a) 870° b)2340° c)7 right angles
4. Find the sum of exterior angles of a polygon with the following
number of sides
a) 7 b) 10 c)250

5.The sides of a hexagon are produced in order. If the
measures of exterior angles so
obtained are (6x-1)° , (10 x+2)°,(8 x+2)°( 9 x-3)°,(5
x+4)° and (12 x+6)°;
Find each exterior angle.
6. The interior angles of a pentagon are in the ratio
4:5:6:7:5. Find each angle of the pentagon.
7.Two angles of a hexagon are 120°and 160°. If the
remaining four angles are equal, find each equal angle.

8.The figure, given below, shows a pentagon ABCDE with
sides AB and ED parallel to each other, and angle B :
angle C : angle D = 5:6:7.
(i)Find the sum of interior angles of the pentagon.
(ii)Write the value of ∠A+∠E
(iii)Find angles B, C and D .
C
A B
C D

More Practice
9. Two angles of a polygon are right angles and the
remaining are 120° each. Find the number of sides in it.
10. In a hexagon ABCDEF, side AB is parallel to side FE
and ∠B:∠C:∠D:∠E=6:4:2:3.find ∠B and ∠D.
11. The angles of a hexagon are x+10°,2x+20°,2x-
20°,3x-50°,x+40° and x+20°. Find x.
12. 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.

Quadrilaterals
Quadrilaterals are 4 sided polygons.

Kite
Definition
A kite is a special quadrilateral with exactly
2 distinct consecutive pairs of sides equal.
Features
• A kite has adjacent sides equal
• No sides parallel
• Diagonals are unequal but
intersect at 90°

Trapezium
Definition
A trapezium is a special quadrilateral with
one pai of parallel sides.
Features
◆ One pair of sides is parallel
◆ One pair of angles is supplementary (co-
interior angles)
◆ A trapezium with non parallel sides equal is
called an isosceles trapezium
◆ A trapezium with 2 right angles
is called a right trapezium.

Parallelogram
Definition
A quadrilateral whose opposite sides are
parallel.
Features
◆ Opposite sides are parallel
◆ Opposite sides are equal
◆ Opposite angles are equal
◆ Adjacent angles are supplementary
◆ Diagonals bisect each other

Rhombus
Definition
It is a special parallelogram with all sides
equal
Features
◆ Opposite sides are parallel
◆ All sides are equal
◆ Diagonal bisect each other at 90°
◆ Diagonals are also the angle bisectors

Rectangle
Definition
A rectangle is a special parallelogram
with all angles equal to 90°
Features
◆ Opposite sides are parallel and
equal
◆ All angles are 90°
◆ Diagonals bisect each other
◆ Diagonal are equal

Square
Definition
A square is a special rectangle that has all
sides equal.
Features
◆ Opposite sides are Parallel
◆ All sides are equal
◆ All angles are 90°
◆ Diagonals are equal
◆ Diagonals bisect each other at 90°
◆ Diagonals bisect the angles of the square

Theorems Related to Special
Quadrilaterals
Theorem 1 - The sum of angles of a quadrilateral
is 360°
Theorem 2 - In a parallelogram
◆ Opposite sides are equal.
◆ Each diagonal bisects the parallelogram

Theorem 3 - The Diagonals of a parallelogram bisect each
other
Theorem 4 – If one pair of sides of a quadrilateral are
equal and parallel. It is a parallelogram.
Theorem 5 – Diagonals of a rectangle are equal and bisect
each other.
Theorem 6 – Diagonals of a rhombus bisect each other at
right angles.
Theorem 7 – Diagonals of a square are equal and bisect
each other at right angles.

Practice Questions - CBSE
1. Fill in the blanks:
◆ A quadrilateral has ……. Sides
◆ A quadrilateral has …… angles.
◆ A quadrilateral has ……. Vertices, no three of which
are……
◆ A quadrilateral has …….. diagonals.
◆ A diagonal of a quadrilateral is a line segment that joins
two ……. Vertices of the quadrilateral.
◆ The sum of the angles of a quadrilateral is ………

2. In the given figure ABCD is a quadrilateral
a) How many pairs of adjacent sides are there? Name them.
b) How many pairs of opposite sides are there? Name them.
c) How many pairs of adjacent angles are there? Name them.
d) How many pairs of opposite angles are there? Name them.
e) How many diagonals are there? Name them.
3. Prove that the sum of the angles of a quadrilateral is 360o
4. The three angles of a quadrilateral are 76o, 54o and 108o. Find the

5. ABCD is a parallelogram in which ∠A=110o. Find the measure of each
of the angles ∠B, ∠C and ∠D.
6. Two adjacent angles of a parallelogram are equal. What is the measure
of
each of these angles?
7. Two adjacent angles of a parallelogram are (3x-4)o and (3x+16)o. Find
the
value of x and hence find the measure of each of its angle.
8. Two sides of a parallelogram are in the ratio 5:3. If its perimeter is
64cm, find the lengths of its sides.
9. The sum of two opposite angles of a parallelogram is 130o. Find the
measure of each of its angle.
10. The perimeter of a parallelogram is 140cm. If one of the sides is

8. Two sides of a parallelogram are in the ratio 5:3.
If its perimeter is 64cm, find the lengths of its sides.
9. The sum of two opposite angles of a
parallelogram is 130o. Find the measure of each of
its angle.
10. The perimeter of a parallelogram is 140cm. If
one of the sides is longer than the other by 10cm,
find the length of each of its sides.

Special Quadrilateral
11. Given a parallelogram ABCD. Complete each
statement along with the definition or property used.
(i) AD = …………
(ii) ∠DCB = ………
(iii) OC = ………
(iv) m∠DAB + m∠CDA = ……..

Special Quadrilateral
12. Consider the following parallelograms. Find the
values of the unknowns x, y, z.

13. Can a quadrilateral ABCD be a parallelogram if
(i) ∠D + ∠B = 180°?
(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
(iii) ∠A = 70° and ∠C = 65°?
14. Draw a rough figure of a quadrilateral that is not a
parallelogram but has exactly two opposite angles of
equal measure.
15. The measures of two adjacent angles of a
parallelogram are in the ratio 3 : 2. Find the measure of
each of the angles of the parallelogram.

16. Two adjacent angles of a parallelogram have equal measure.
Find the measure of each of the angles of the parallelogram.
17. The adjacent figure HOPE is a parallelogram. Find the angle
measures x, y and z. State the properties you use to find them.

18. The following figures GUNS and RUNS
are parallelograms. Find x and y. (Lengths are
in cm)

19. In the above figure both RISK and CLUE
are parallelograms. Find the value of x.

20. Explain how this figure is a trapezium.
Which of its two sides are parallel?

21. Find ∠C in below figure if AB || DC
22. Find the measure of ∠P and ∠S if PS || RQ in figure. Is there
any other method to find ∠P?

More Practice - CBSE
1. In parallelogram PQRS, ∠Q = (4x – 5)° and
∠S = (3x + 10)° . Calculate: ∠Q and ∠R.
2. In rhombus ABCD: If ∠A=74°; find ∠B and
∠C.
3.In square PORS:
(i) If PQ = 3x – 7 and QR = x + 3; find PS
(ii) PR = 5x and QR = 9x – 8

4. ABCD is a rectangle, if ∠BPC = 124°
Calculate: (i) ∠BAP (ii) ∠ADP
5. ABCD is a rhombus. If ∠BAC = 38°, find:
(i) ∠ACB
(ii) ∠DAC
(iii) ∠ADC

6. ABCD is a rhombus. If ∠BCA = 35°. Find ∠ADC.
7. PQRS is a parallelogram whose diagonals
intersect at M. ∠PMS=54°, ∠OSR=25° and
∠SOR=30°;
(i) ∠RPS
(ii) ∠PRS
(iii) ∠PSR

8. In an isosceles-trapezium, show that the
opposite angles are supplementary.
9. The angles of a quadrilateral are in the ratio of
2 : 3 : 5 : 8. Find the measure of each angle.
10. In the given figure ABCD, find the value of x.

11.In the given figure, ABCD is a
parallelogram. Find x, y and z
12. Find x in the following figure.
13. In the given parallelogram ABCD, find the
value of x and y

14. Find the values of x and y in the following
parallelogram

15. Write true and false against each of the given
statements.
(a) Diagonals of a rhombus are equal.
(b) Diagonals of rectangles are equal.
(c) Kite is a parallelogram.
(d) Sum of the interior angles of a triangle is 180°.
(e) A trapezium is a parallelogram.
(f) Sum of all the exterior angles of a polygon is 360°.
(g) Diagonals of a rectangle are perpendicular to each
other.
(h) Triangle is possible with angles 60°, 80° and 100°.

Objective questions
1. The two diagonals are not necessarily
equal in a
(a)rectangle
(b)square
(c) rhombus
(d) isosceles trapezium

2. The length of the diagonals of a
rhombus are 16cm and 12cm. The
length of each side of the rhombus
is
(a)8cm
(b)9cm
(c)10cm
(d)12cm

3. Two adjacent angles of a
parallelogram are (2x+25)0 and (3x-
5)0. The value of x is
(a)28
(b)32
(c)36
(d)42

4. The diagonals do not necessarily
intersect at right angles in a
(a)parallelogram
(b)rectangle
(c)rhombus
(d)kite

5. The length and breadth of a
rectangle are in the ratio 4:3. If the
diagonal measures 25cm then the
perimeter of the rectangle is
(a)56cm
(b)60cm
(c)70cm
(d) 80cm

Draw triangles, quadrilaterals, and regular polygons (5, 6, 8, or 10 sides) with given angle measures.

More Related Content

What's hot (20)

Similar to Draw triangles, quadrilaterals, and regular polygons (5, 6, 8, or 10 sides) with given angle measures. (20)

Recently uploaded (20)

Draw triangles, quadrilaterals, and regular polygons (5, 6, 8, or 10 sides) with given angle measures.