Which among the following has the most number of diagonals?

A.

Triangle

B.

C.

Pentagon

D.

Can't be determined

#### SOLUTION

Solution : C

The pentagon has the most number of vertices among the options. Hence, it has the most number of diagonals.

In the given diagram, the value of x is ___ degrees. #### SOLUTION

ABC+BCD+CDA+DAB=36040+50+CDA+70=360CDA+160=360CDA=360160=200
Now, CDA+ADC=360 ( Angle at a point)
200+x=360x=360200x=160

In a concave polygon, no part of any of their diagonals is external.

A.

True

B.

False

#### SOLUTION

Solution : B

A concave polygon will have some part of at least one diagonal external.

Which of the following are definitely regular polygons?

A.

Triangle

B.

Square

C.

Rhombus

D.

Rectangle

#### SOLUTION

Solution : B

A regular polygon is a polygon which is equiangular i.e. all the angles are equal and equilateral i.e. all the sides are equal.

The triangle if equilateral is a regular polygon. If not, it is not a regular polygon.

A rhombus has equal sides but not equal angles.

A Rectangle has equal angles but not equal sides. Hence, they are not regular polygons.

A square has equal sides and equal angles. Hence, it is a regular polygon.

Which of the following is true?

A.

All squares are rectangles

B.

All rectangles are squares

C.

All rectangles are rhombuses

D. None of the above

#### SOLUTION

Solution : A

The statement that all squares are rectangles is true because a square is a special type of rectangle where, the adjacent sides are equal.

If ABCD is a parallelogram, then the angle bisectors of A and D meet at ‘O’. The measure of AOD is 45

A.

True

B.

False

#### SOLUTION

Solution : B LetA=x
then D=(180x)
(Since the adjacent angles of a parallelogram sum up to 180)

A2=x2=DAO

In ΔAOD,

AOD+ADO+DAO=180   [Angle sum property of a triangle]
AOD=180[x2+90x2]
or AOD=18090=90
The measure of AOD is 90

Which of the following is not a model for a plane surface?

A.

Top surface of table

B.

Surface of paper

C.

Body of car

D.

None of these

#### SOLUTION

Solution : C

The body of a car is a 3 dimensional surface. It is not a plane 2 dimensional surface

A quadrilateral with two distinct pairs of equal-length adjacent sides is known as

A. Rhombus
B. Trapezium
C. Parallelogram
D. Kite

#### SOLUTION

Solution : D

A quadrilateral with two distinct pairs of equal-length adjacent sides is known as a kite. Two sides of a kite have lengths 7.8 cm and 11 cm. Then the perimeter of the kite is

A. 45.5 cm
B. 48.3 cm
C. 37.6 cm
D. 55 cm

#### SOLUTION

Solution : C

Let ‘a’ be one side of the kite = 7.8 cm
and‘b’ be the other side of the kite = 11 cm

Perimeter of the kite = 2a + 2b units
=2×7.8+2×11=15.6+22=37.6 cm

Which of the following is true?

A.

All parallelograms are kites

B.

All kites are parallelograms

C.

Some kites are parallelograms

D. None of the above

#### SOLUTION

Solution : C

The kites that have all the sides equal and two pairs of sides parallel are parallelograms. These kites are rhombuses.

Hence, some kites are parallelograms.