Question

Q1. The interior angle of regular polygon is 156o. Find the number of sides of the polygon. Q2. How many sides does a regular polygon have if the measure of an exterior angle is 24o ? Q3. What is the measure of each angle of regular hexagon? Q4 Find ten rational numbers between −2/5 and 1/2 Q5.What must be added to −1/2 to get 5/16 Q6. Kanwar is three years older than Amina. Six years ago, Kanwar’s age was four times Amina’s age. Find the age of Kanwar and Amina. Q7. The Sum of two numbers is 45 and their ratio is 7:8. Find the numbers. Q8. The length of a rectangle exceeds its breadth by 4 cm. If length and breadth are each increased by 3cm, the area of the new rectangle will be 81 sq. cm more than that of the given rectangle. Find the length and breadth of the given rectangle. Q9. A quadrilateral has three acute angles, each measure 800. What is the measure of the fourth angle? Q10. The angles of a quadrilateral are in the ratio 1:2:3:4. What is the measure of the four angles?

Answer 1

Answer:

1. Interior angle = 156°

Exterior angle of the polygon = 180-156

                                                 = 24

∴ Exterior angle = 24°

No. of sides the polygon has = 360/ each exterior angle

                                                = $\frac{360}{24}$

                                                = 15 sides

∴ The polygon has 15 sides

2. Exterior angle = 24°

No. of sides = 360/ each exterior angle

                    = $\frac{360}{24}$

                    = 15

∴ The polygon has 15 sides

3. No. of sides a hexagon has = 6 sides

Measure of each exterior angle = 360/ no. of sides

                                                    = $\frac{360}{6}$

                                                    = 60°

∴ The measure of each exterior angle of a hexagon = 60 °

Measure of each interior angle = 180 - 60

                                                   = 120 °

∴ The measure of each angle of a regular hexagon = 120°

4. $\frac{-2}{5}$   and   $\frac{1}{2}$

$\frac{-2}{5}$  X $\frac{4}{4}$ = $\frac{-8}{20}$

$\frac{1}{2}$  X  $\frac{10}{10}$ =  $\frac{10}{20}$

No.s between $\frac{-2}{5}$   and  $\frac{1}{2}$  is equal to numbers between $\frac{-8}210}$  and $\frac{10}{20}$

Rational numbers between $\frac{-2}{5}$  and $\frac{1}{2}$  are :

$\frac{-7}{20} , \frac{-6}{20} , \frac{-5}{20}, \frac{-4}{20} , \frac{-3}{20} , \frac{-2}{20} , \frac{-1}{20} , \frac{1}{20} , \frac{2}{20} , \frac{3}{20}$

5. Let the missing number be 'X'

The first number = $\frac{-1}{2}$

The sum of the two numbers = $\frac{5}{16}$

$\frac{-1}{2}$  +  X  = $\frac{5}{16}$

X = $\frac{5}{16} - (\frac{-1}{2})$

X =  $\frac{5}{16} - (\frac{-8}{16})$

X = $\frac{5 + 8}{16}$

X = $\frac{13}{16}$

∴ The number to be added is  $\frac{13}{16}$.

6. Let Amina's present age be 'x'

Kanwar's present age = x + 3

Age of Amina 6 years ago = x - 6

Age of Kanwar 6 years = 4 ( x - 6 ) = 4x - 24

( x + 3 - 6) = 4x - 24

x -3 = 4x - 24

x - 4x = -24 + 3

-3x = -21

x = $\frac{-21}{-3}$

x = 7

∴ Amina's current age = x = 7 years

∴ Kanwars age = x + 3 = 7 + 3 = 10 years

7.  Let the numbers be 7x and 8x

Sum of the numbers = 45

7x + 8x = 45

15x =45

x = $\frac{45}{15}$

x = 3

∴ The first number = 7x = 7 x 3 = 21

∴ The second number = 8x = 8 x 3 = 24

∴The numbers are 21 and 24 respectively.

8. Let the breadth be 'b'

∴ The length = b + 4

Area of the rectangle = l x b

                                   = b (b+4)

                                   = $b^{2}$ + 4b

If the area of the length and breadth are increased by 3

Length = b + 4 + 3 = b + 7

Breadth = b + 3

Area of rectangle = l x b

                       81  = ( b + 7 )  x  ( b + 3 )

                       81 = ( $b^{2}$ + 10b + 21)

$b^{2}$ + 10b + 21 = ($b^{2}$ + 4b) + 81

($b^{2} - b^{2}$ ) +  10b - 4b = 81 - 21

6b = 60

b = $\frac{60}{6}$

b = 10cm

∴ Breadth of the rectangle = b = 10cm

∴ Length of the rectangle = b + 4 = 10 + 4 = 14 cm

∴ The length and breadth of the rectangle are 14cm and 10cm respectively.

9. Given.

Measure of the three angles = 80° each

Let the measure of the the fourth angle be 'x'

Sum of angles of a polygon = 360°

80 + 80 + 80 + x = 360

240 + x = 360

x = 360 - 240

x = 120°

∴ The measure of the fourth angle = 120°

10. Let the angles of the quadrilateral be x, 2x, 3x and 4x

Sum of angles of a quadrilateral = 360

x + 2x + 3x + 4x = 360

10x = 360

x = $\frac{360}{10}$

x = 36

Angles of the quadrilateral are :

x = 36°

2x = 36 x 2 = 72°

3x = 3 x 36 = 108°

4x = 4 x 36 = 144°

∴ The measures of the angles are 36°, 72°, 108° and 144°