As the angles are in the ratio 2:5:4:1, they can be written as-

2x, 5x, 4x, and x

Now, as the sum of the angles of a quadrilateral is 360°,

2x + 5x + 4x + x = 360°

Or, x = 30°

Now, all the angles will be,

2x =2 × 30° = 60°

5x = 5 × 30° = 150°

4x = 4 × 30° = 120°, and

x = 30

Let the angle of the parallelogram given in the question statement be “x”.

Now, its adjacent angle will be 2x.

It is known that the opposite angles of a parallelogram are equal.

So, all the angles of a parallelogram will be x, 2x, x, and 2x

As the sum of interior angles of a parallelogram = 360°,

x + 2x + x + 2x = 360°

Or, x = 60°

Thus, all the angles will be 60°, 120°, 60°, and 120°.

In a trapezium ABCD, A + D = 180° and B + C = 180°

So, 55° + D = 180°

Or, D = 125°

Similarly,

70° + C = 180°

Or, C = 110°

It is known that the sum of angles of a quadrilateral is always 360°. To have all angles as obtuse, the angles of the quadrilateral will be greater than 360°. So, it is not possible to draw a quadrilateral whose all angles are obtuse angles.

Let ABCD be a rectangle where AC and BD are the two diagonals which are intersecting at point O.

Now, assume BDC = 25° (given)

Now, BDA = 90° – 25° = 65°

Also, DAC = BDA, (as diagonals of a rectangle divide the rectangle into two congruent right triangles)

So, BOA = the acute angle between the two diagonals = 180° – 65° – 65° = 50°

 Surface area:
Surface area of a solid object is a measure of the total area that the surface of the object occupies and it is always measured in square unit.

 

Hence surface area is also known as total surface area TSA.

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Given:

Dimension of brick = l=22.5 cm, b=10 cm, c=7.5 cm

 

Total surface area of a container= 9.375 m²

Total surface area of a brick = 2(lb + bh + lh)


= 2(22.5×10 + 10×7.5 + 22.5×7.5)


= 2(225 + 75 + 168.75)


= 2×468.75

 = 937.5 cm²

= 937.5/100×100 m²


Number of bricks that painted out of this container= total area painted by containers paint / total surface area of a brick

 

=9.375/ (937.5/100×100)

 =( 9.375×100×100) / 937.5

= 937500/ 9375= 100

Hence,100 bricks can be painted out.

The length of the each side of water tank $=1.5m=150cm$

As it is given that base is not covered with tiles so, five sides of the tank are 

covered with tiles.

Therefore,

Surface area of water tank $=5a^2=5(150{)}^2=112500c{m}^2$

Side of tile $=25cm$

Area of tile $=25^2=625c{m}^2$

Number of tiles to cover five sides of the tank $=\frac{112500}{625}=180$

Now,

Cost of one dozen tiles $=Rs.360$

Hence, total cost of $180=\frac{360}{12}\times 180=Rs.5400$

Let’s arrange the data given in ascending order – 44, 45, 49, 50, 52, 55, 60.

n= 7, so it’s an odd number

Median = (n+1) / 2 observations

= (7+1)/ 2 = (8/2)^th observation = 4th observation = 50 kg

Let’s arrange the data given in ascending order – 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 29,31,35.

n= 13, so it’s an odd number

Median = (n+1) / 2 observations

= (13+1)/ 2 = (14/2)^th observation = 7th observation = 23