Question 1 :
The number sides of two regular polygons are in the ratio 2 : 1 and their interior angles are in the ratio 4 : 3. Find the number of sides in each polygon.

Question 2 :
Find the number of sides in a regular polygon, if its each interior angle is $160^{\circ}$.

Question 3 :
In a regular polygon, the exterior and interior angles are in the ration $1 : 4$. The number of sides of the polygon is

Question 4 :
One angle of a six-sided polygon is $140^{\circ}$ and the other angles are equal. Find the measure of each equal angle.

Question 5 :
The interior angles of a regular polygon are each $165^o$. How many sides does the polygon have?

Question 6 :
The measurement of each angle of a polygon is 160$^{\circ}$. The number of its sides is?<br/>

Question 7 :
How many sides does a regular polygon have, if measure of each of its interior angle is ${160}^{o}$?

Question 8 :
<span>Is it possible to have a polygon, whose sum of interior angles is&#160;</span><span>$870^{\circ}$</span><div>Answer: No<br/>State true or false:<br/><br/></div>

Question 9 :
Three angles of a seven sided polygon are $\displaystyle 132^{\circ}$each and the remaining four angles are equal. Find the value of each equal angle.

Question 11 :
if $\hat { i } +2\hat { j } +3\hat { k } $ and $ 3\hat { i } -2\hat { j } +\hat { k } $ are the adjacent sides of a parallelogram, then its area will be&#160;

Question 12 :
A field is in the form of a rhombus has each side of length 81 m and altitude 16 m. The side of a square field which has the same area as that of the rhombus is

Question 13 :
The perimeter of a rhombus is 40 cm and the length of one of its diagonals is 12 cm then the area of the rhombus is

Question 14 :
Which of the following is the correct match with respect to the given question ?<br>'ABCD' is a rhombus such that $ \angle ACB=40^o$ then $\angle ADB =$____.<br><table class="wysiwyg-table"><tbody><tr><td>$70^o$</td><td>As $\angle ADB=1/2 (180^o-40^o)$</td></tr><tr><td>$45^o$</td><td>$\angle C+\angle D=90^o$</td></tr><tr><td>$50^o$</td><td>$\angle BCD=80^o\Rightarrow \angle ADC=100^o \therefore \angle ADB=(1/2)x 100^o$</td></tr><tr><td>$60^0$</td><td>All sides are equal</td></tr></tbody></table>

Question 15 :
Find the area of a trapezoid with bases of $21$and $17$ mm, and a height of $10$ mm.<br/>

Question 16 :
Find the measure of all the angles of a parallelogram, if one angle is $24^{\circ}$ less than twice the smallest angle.

Question 17 :
<div><span>$ABCD$ is a parallelogram of area $162\ sq. cm$. $P$ is a point on $AB$ such that $AP : PB = 1 : 2$.&#160;</span><br/><span>Calculate </span><span>the ratio $PA : DC$.</span></div>

Question 18 :
The perimeter of a rhombus is $100$ cm and one of its diagonals is $40$ cm . Then the area of the rhombus in square centimeters is

Question 19 :
The difference between the two parallel sides of a trapezium is $8 m$. The perpendicular distance between them is $24 m$. If the area of the trapezium is $312 m^{2}$, then what are the lengths of the two parallel sides?

Question 20 :
<span>The area of a rhombus is $216 sq. cm$. If its&#160;one diagonal is $24 cm$, find the&#160;</span>length of its other diagonal.