Understanding Quadrilaterals Class 8 Worksheet Maths Chapter 3

Multiple Choice Questions (MCQs)

Q1:How many sides does a regular polygon have if each of its interior angles is 165°?

A) 20
B) 22
C) 24
D) 26

Ans. C)

Sol:Total sum of all the exterior angles of a regular polygon = 360°

Let number of sides be $n$n.

Measure of each interior angle = 165°

Measure of each exterior angle = $180°\; -\; 165°\; =\; 15°$180° − 165° = 15° [Since an interior and an exterior angle forms a linear pair]

Number of sides = Sum of exterior angles / Each exterior angle

$=\; \backslash frac\{360°\}\{15\}$=360°/15 = 24

Q2: What will be the sum of interior angles of a polygon having 8 sides?

A) 720°
B) 1080°
C) 1260°
D) 1440°

Ans.B)

Sol: Sum of interior angles of polygon=(2n−4)⋅90
=(16−4)⋅90
=12 x 90
$=\; 1080$=1080°

Q3: Find out the number of sides of a regular polygon whose exterior angles are 60°.

A) 3
B) 4
C) 6
D) 12

Ans.C)

Sol: External Angle of a Regular Polygon = 360° / Total number of sides. 
⇒ n × 60° = 360° gives n = 6.

Q4: The sides of a quadrilateral are in the ratio of 2:5:4:1. Find out the smallest angle.

A) 120°
B) 180°
C) 60°
D) 90°

Ans.C)

Sol: Let the first angle be = 2x
Let the second angle be = 5x
Let the third angle be = 4x
Let the fourth angle be = 1x (from the ratio given)
We know that the sum or addition of all the angles which are interior in the quadrilateral gives a total answer as 360°. 
Therefore, 
2x+5x+4x+1x = 360°
$=>\; 12x\; =\; 360°$12x = 360°
x = 360/12 
x= 30
The measure of all the interior angles of the quadrilateral

Q5: What is the name of a regular polygon of 3 sides?
A) Equilateral triangle
B) Square
C) Regular hexagon
D) Regular octagon

Ans. A)

Sol:A regular polygon of 3 sides is a triangle where all sides and angles are equal. This type of triangle is called an Equilateral Triangle.

True/False

Q1: A regular octagon has 1080 degree of total sum of interior angle.

Ans. True 

Sol:Sum of interior angles = (n−2)×180°
Here, n=8.
Sum of interior angles = (8−2)×180°

=6×180° = 1080°

Q2: A regular polygon with exterior angles of 80° has 7 sides.

Ans. False

Sol:
Therefore, regular polygon cannot have 7 sides if each exterior angle is 80°

Q3: A parallelogram has all the sides equal.

Ans. False 

Sol:  A parallelogram is a quadrilateral where opposite sides are parallel and equal in length. However, not all sides need to be equal. If all sides of a parallelogram are equal, it becomes a rhombus, which is a special type of parallelogram.

So, not all parallelograms have all sides equal.

Q4: Exterior angle sum of hexagon is 360°

Ans. True

Sol: The sum of the exterior angles of any polygon (regular or irregular) is always 360°, regardless of the number of sides.

Q5:  The measure of exterior angle of regular polygon is 40°

Ans. True

Sol:

Very Short Answer Questions

Q1: Write down the formula of area of rhombus.

Ans. ½ × product of diagonals

Q2:  Can all the angles of a quadrilateral be right angles?

Ans. Yes, all the angles of a quadrilateral can be right angles.

Q3:  Name the quadrilateral whose diagonals are equal.

Ans.Square, rectangles

Q4: Each angle of a square measures ___°.

Ans.90°

Q5: How many parallel lines are in a trapezium?

Ans. 2

Q6: Which figure is equiangular and equilateral polygons?

Ans.Square, Triangle 

Q7: A parallelogram can be rectangle if measure of each angle is _______.

Ans.90 degrees 

Q8: If the diagonals of a quadrilateral are perpendicular bisectors of each other then it is always a______.

Ans. Rhombus

Q9: The sum of all angles in a quadrilateral is equal to_____ right angles.

Ans. 4

Short Answer Questions

Q1:ABCD is a parallelogram in which ∠A=110°. Find the measure of the angles B, C and D, respectively.

Ans. The measure of angle A=110°

The sum of all adjacent angles of a parallelogram is 180°

∠A + ∠B = 180

110°+ ∠B = 180°

∠B = 180°- 110°
= 70°.

Also ∠B + ∠C = 180° [Since ∠B and ∠C are adjacent angles]

70°+ ∠C = 180°

∠C = 180°- 70°

= 110°.

Now ∠C + ∠D = 180° [Since ∠C and ∠D are adjacent angles]

110o+ ∠D = 180°

∠D = 180°- 110°

= 70°

Q2:The two adjacent angles of a parallelogram are the same. Find the measure of each and every angle of the parallelogram.

Ans. A parallelogram with two equal adjacent angles.

To find:- the measure of each of the angles of the parallelogram.

The sum of all the adjacent angles of a parallelogram is supplementary.

∠A+∠B=180°

2∠A = 180°

∠A = 90°

∠B = ∠A = 90°

In a parallelogram, the opposite sides are the same.

Therefore,

∠C=∠A=90°

∠D=∠B=90°

Hence, each angle of the parallelogram measures 90°.

Q3: If three angles of a trapezium is 50°, 130° and 120°. Then find the other angle.

Ans.Given that the angles are 50 degrees, 130 degrees, and 120 degrees, you can find the fourth angle as follows:

Let the fourth angle be "x" degrees.

Given angles: 50°, 130°, 120°, x°

Since the sum of all angles of a quadrilateral is :

50°+130°+120° + x° = 180°

300 + x° = 180°

Now solving for "x":

x° = 360° - 300°

x° = 60°

So, the fourth angle in the trapezium is 60 degrees.

Q4: If two adjacent angles of a parallelogram are in the ratio 2:3 Find all the angles of the parallelogram.

Ans.Let P=2x and Q=3x
Since sum of all the angles of parallelogram is 360°
So, 2x + 3x =180°
5x=180°
x=180°/5
Therefore x=36°
So, P=2x 
=> P=72° 
and Q=3x 
=> Q=108°
So R= 72° {angle opposite of P}
S=108° {angle opposite of Q}

Q5: If the angles of a quadrilateral are in the ratio 3:6:8:13. The largest angle is?

Ans.Let the angles are $3x,\; 6x,\; 8x,\; 13x$3x,6x,8x,13x.

$3x\; +\; 6x\; +\; 8x\; +\; 13x\; =\; 360°$Since sum of all the angles of Quadrilateral is 360°
3x+6x+8x+13x=360°
$30x\; =\; 360°$30x=360°
x=12°

Thus, the largest angle is 156°.

Q6: The angles of a quadrilateral are x°, x+5°, x+10°, x+25°. Then find the value of x.

Ans.Since sum of all the angles of Quadrilateral is 360°
Therefore,
x+(x+5)+(x+10)+(x+25)=360°
x+x+5+x+10+x+25=360
4x+40=360°
4x=360°−40°
4x=320°
x=320°/4 
x=80°