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QUESTION: 1

What is the sum of angles of quadrilaterals?

Solution:

QUESTION: 2

The opposite angles of a parallelogram are (3x – 2)° and (50 – x)° the measure of these angles is

Solution:

The opposite angles in a parallelogram are equal.

So,1st angle=2nd anlge

- 1st angle = 3x-2
- 2nd angle = 50-x

so, equate both the angles

3x-2=50-x

3x+x=50+2

4x=52

x=52/4

x=13

now, substitute the value of x

therefore,

1st angle = 3x-2

1st angle = 39-2 = 37^{o}

2nd angle = 50-x

2nd angle = 50-13 = 37^{o}

QUESTION: 3

The diagonals of a rhombus are 10 cm and 24 cm. find the length of a side of the rhombus.

Solution:

We know that in a rhombus the diagonals bisect each other at 90∘90∘

AC=24cm

AD=12cm

BD=10cm

BO=5cm

AB^{2}=AD^{2}+OB^{2}

=12^{2}+5^{2}

=144+25

=169

AB=√169

=13cm

Hence the length of the rhombus is 13 cm

QUESTION: 4

In quadrilateral PQRS, if ∠P = 60° and ∠Q : ∠R : ∠S = 2 : 3 : 7, then ∠S =

Solution:

Let ∠Q = 2x, ∠R = 3x and ∠S = 7x

Now, ∠P + ∠Q + ∠R + ∠S = 360°

⇒ 60° + 2x + 3x + 7x = 360°

⇒ 12x = 300°

⇒ x = 300°/ 12 = 25°

∠S = 7x = 7 × 25° = 175°

QUESTION: 5

Which of the following is not a parallelogram?

Solution:

Both trapezium and parallelogram are quadrilaterals. A parallelogram has two pairs of parallel sides. A trapezoid only has one pair of parallel sides.

Hence, the answer is Trapezium.

QUESTION: 6

The angles of a quadrilateral are (5x)°, (3x + 10)°, (6x – 20)° and (x + 25)°. Now, the measure of each angle of the quadrilateral will be

Solution:
Sum of all angle of quadrilateral=360dgree

5x+3x+10+6x-20+x+25=360

=15x+15=360

=15x=360-15

=15x=345

=x=23

First angle=5x=5×23=115

Second angle=3x+10=3×23+10=79

Third angle=6x-20=6×23-20=118

Fourth angle=x+25=23+25=48.(Ans).

5x+3x+10+6x-20+x+25=360

=15x+15=360

=15x=360-15

=15x=345

=x=23

First angle=5x=5×23=115

Second angle=3x+10=3×23+10=79

Third angle=6x-20=6×23-20=118

Fourth angle=x+25=23+25=48.(Ans).

QUESTION: 7

The angles of a quadrilateral are in the ratio 3:5:9:13. The measure of angles of quadrilateral are:

Solution:

QUESTION: 8

Two angles of a quadrilateral are 50° and 80° and other two angles are in the ratio 8 : 15. Find the measure of the remaining two angles.

Solution:
Let the other two angles be 8x and 15x

{by angle sum property of a quadrilateral=360०}

solution= 80०+50०+8x+15x=360०

130०+23x=360०

23x =360०-130०

=230०

23x=230०

x=230÷23

x=10

putting the value of x =10

8x = 8×10=80

15x=15×10=150

so other two angles which is in ratio 8:15 is

8o० and 150०

{by angle sum property of a quadrilateral=360०}

solution= 80०+50०+8x+15x=360०

130०+23x=360०

23x =360०-130०

=230०

23x=230०

x=230÷23

x=10

putting the value of x =10

8x = 8×10=80

15x=15×10=150

so other two angles which is in ratio 8:15 is

8o० and 150०

QUESTION: 9

All the angles of a convex quadrilateral are congruent. However, not all its sides are congruent. What type of quadrilateral is it?

Solution:

All the angles of a convex quadrilateral are congruent .

∴ Each angle = 90^{0}

Thus, the quadrilateral can be either square or rectangle.

Since all the sides are not equal, the quadrilateral is a rectangle because in rectangle only opposite sides are equal.

QUESTION: 10

The type of polygon in which its all angles and sides are equal is classified as

Solution:
A polygon in which all sides are equal is called equilateral polygon and a polygon in which all angles are equal is called equiangular polygon polygon in which all sides and all angles are equal is called a regular polygon so the answer will be regular polygon

### Examples: Angle Sum Property of a Triangle

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### Angle Sum Property of all Polygons

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### Examples: Angle Sum Property of Triangle

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### Angle Sum Property of a Quadrilateral

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