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The sum of the interior angles of a regular polygon is twice the sum of the exterior angles. Find the number of sides of the polygon

Let n be the sides,then $(n-2) \times 180 = 2 \times 360$ $n=6$

Three angles of the quadrilaterals are in the ratio 2:3:4. The sum of the least and the greatest of these three angles is equal to 180°. Find all the angles of the quadrilateral

Three angles of the quadrilaterals are in the ratio 2:3:4, then it will be 2x,3x,4x.

Now it is given

$2x + 4x=180$

$x=30$

So three angles are 60°,90°,120°

Let y be the fourth angle,Now in a quadrilateral

Sum of all angles =360

$y + 60+90+120=360$

$y=90$

So All the four angles are 60°,90°,120°,90°

The exterior angle of a regular polygon is one-fifth of its interior angle. How many sides has the polygon?

let the interior angle be x,then exterior angle will be (180- x )

Now as per the question

$(180 - x ) = \frac {1}{5} x$

Solving this, we get

x= 150°

Therefore,Each interior angle is 150°

Now we know that

Sum of all interior angles is given by =$( n - 2 ) \times 180$

Therefore

$( n - 2 ) \times 180 = 150 n$

Simplifying this we get

6n - 5n = 12

n = 12

So, Number of sides= 12

One of the angle in the parallelogram is 80°. Find the other angles in the parallelogram

Adjacent angles are supplementary, So

$x + 80=180$

x=100°
So angles are 80°,100°,80°, 100°

The angles of the quadrilateral is in the ratio 1:2:3:4. Find all the angles

Let x be common ratio, then angles are 1x,2x,3x,4x

Sum of all angles =360

$1x+2x+3x+4x=360$

$x=36$

So angles are 36°, 72°, 108°,144°

One of the diagonals of a rhombus is equal to its sides. Find the measures of all the angles of the rhombus

Here AB=BC=CD=AD

Also AB=AC

Now in Triangle ABC,

AB=BC=AC

Hence equliateral triangle

$\angle B=60$, $\angle BAC=60$ and $\angle BCA=60$

Now in Triangle ACD

AC=CD=AD

Hence equliateral triangle

$\angle D=60$, $\angle DAC=60$ and $\angle DCA=60$

Now $\angle A= \angle BAC + \angle DAC=120$

$\angle C =\angle BCA + \angle DCA=120$

Hence angles are 60°, 120°, 60°,120°

In a parallelogram ABCD, the bisectors of ∠ A and ∠ B meet at O. Find ∠ AOB.

Find the value of x in the trapezium ABCD

Since DC and AB are parallel , these angles are supplementary

$x-22 + x + 42=180$

$2x + 20 =180$

$x=80$

The diagonals of a rhombus are 8 cm and 15 cm. Find its side.

Since diagonals bisect each other and are Perpendicular,Side is given by pythagorus theorem as

$a= \frac {1}{2} \sqrt {d_1^2 + d_2^2} = 8.5$ cm

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

Oppossite angles are equal

So 6y=120, y=20

Now adjacent angles are supplementary

$120 + 5x + 10=180$

$x=10$

This Understanding Quadrilaterals Class 8 Extra Questions is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feebback on the mail. You can download this also using the below link

**Notes****NCERT Solutions**

Class 8 Maths Class 8 Science