Understanding Quadrilaterals Test

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Understanding Quadrilaterals Test - 27

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Weekly Quiz Competition

Question 1
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If the two adjacent angles of a parallelogram are $$(3x-20^\circ)$$ and $$(50^\circ -x)$$, then the value of $$x$$ is:

A
$$55^\circ$$

B
$$75^\circ$$

C
$$20^\circ$$

D
$$80^\circ$$

Solution

We know that sum of adjacent angles of a parallelogram is $$180^o$$.
Therefore,
$$(3x-20^o)+(50^o-x)=180^o$$
$$2x+30^o=180^o$$
$$2x=150^o$$
$$x=75^o$$
Option B is correct.
Question 2
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If an angle of a parallelogram is four-fifths of its adjacent angle, what are the angles of the parallelogram?

A
$$60^o, 120^o, 60^o, 120^o$$

B
$$90^o, 90^o,90^o,90^o$$

C
$$80^o, 100^o,80^o,100^o$$

D
$$30^o, 150^o, 30^o, 150^o$$
Question 3
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A parallelogram and a triangle stand on the same side of the base with the same base and on the same side of the base with the same height. If $${l}_{1}$$, $${l}_{2}$$ be the perimeters of the parallelogram and the rectangle respectively, then the which one of the following is correct?

A
$${l}_{1}< {l}_{2}$$

B
$${l}_{1}={l}_{2}$$

C
$${l}_{1}> {l}_{2}$$ but $${l}_{1}\ne 2{l}_{2}$$

D
$${l}_{1}=2{l}_{2}$$
Question 4
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A school was having 4 Hexagonal buildings joined to each other. They wanted to utilize the space between the 4 buildings to make a playground. The shape is that of a parallelogram. Can you find the measure of the angles as opposite angles are equal?

A
$$60^o, 120^o$$

B
$$20^o, 60^o$$

C
$$80^o, 120^o$$

D
$$40^o, 40^o$$

Solution

$$x$$ and $$y$$ are exterior angles of the regular polygon.
$$\displaystyle \frac{360}{6} = 60$$ i.e value of $$x$$ angle
Opposite angles are $$60^o+60^o$$
$$360^o - 120^o (60^o + 60^o)$$
$$360^o = 60^o + 60^o + y + y$$
$$2y = 360^o - 120^o$$
$$y =$$ $$ \dfrac{240^o }{ 2}$$
$$y = 120^o$$
Therefore, option A is the correct answer.
Question 5
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Which of the following statement(s) is/are correct ?

A
A parallelogram in which two adjacent angles are equal is a rectangle.

B
A quadrilateral in which both pairs of opposite angles are equal is parallelogram

C
In a parallelogram the number of acute angles is two.

D
All of these

Solution
Question 6
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The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.
What is the length of the diagonal SQ?

A
$$\sqrt{7}$$

B
$$\sqrt{8}$$

C
$$\sqrt{6}$$

D
$$\sqrt{5}$$
Question 7
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In a parallelogram $$ABCD$$, if $$AB = 2x + 5, CD = y + 1, AD = y + 5$$ and $$BC = 3x - 4$$, what is the ratio of $$AB$$ and $$BC$$?

A
$$71 : 21$$

B
$$12 : 11$$

C
$$31 : 35$$

D
$$4 : 7$$

Solution

In parallelogram, opposite sides are parallel and equal
$$\therefore AB=CD$$ and $$AD=BC$$
$$\Rightarrow 2x+5=y+1\longrightarrow 1$$
$$\Rightarrow 3x-4=y+5\longrightarrow 2$$
Equation 2-equation 1
$$\left( 3x-2x \right) -4-5=0+4$$
$$x=13$$
Put value of x in 1
$$2(13)+5-1=y$$
$$y=30$$
$$\cfrac { AB }{ BC } =\cfrac { 2x+5 }{ 3x-4 } =\cfrac { 2(13)+5 }{ 3(13)-4 } $$
$$\cfrac { AB }{ BC } =\cfrac { 31 }{ 35 } $$
$$\therefore AB:BC=31:35$$
Question 8
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In the given figure, ABCD is a parallelogram, AL $$\perp$$ BC, AM$$\perp$$ CD, AL$$=4$$cm and AM$$=5$$cm. If BC$$=6.5$$cm, then find CD.

A
$$5.2$$cm

B
$$8.7$$cm

C
$$6.5$$cm

D
$$3.3$$cm

Solution
Question 9
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Which of the following closed plane figures is/are not polygons?

A

B

C

D

Solution
Question 10
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A parallelogram with all equal sides are called _________.

A
Rhombus

B
Rectangle

C
Polygon

D
None of these

Solution