### MCQ on understanding Quadrilaterals:

The diagonals do not necessarily bisect the interior angles at the vertices in a

(a) rectangle

(b) square

(c) rhombus

(d) all of these

In figure, ABCD is a trapezium in which side AB is parallel to side DC and E is the midpoint of side AD. If F is a point on side BC such that the segment EF is parallel to side DC, then the value of EF is equal to

(a) 1/4(AB + DC)

(b) 1/2(AB + DC)

(c) 1/3(AB + DC)

(d) 2/3(AB + DC)

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Three angles of a quadrilateral are 54º, 80º and 116º. Find the measure of the fourth angle.

(a) 70^{o}

(b) 90^{o}

(c) 110^{o}

(d) 120^{o}

The sum of angles of a quadrilateral is _____ right angles.

(a) four

(b) two

(c) one

(d) none of these

In the adjoining figure, AP and BP are angle bisectors of ∠A and ∠B which meet at P of a parallelogram ABCD. Then 2∠APB =

(a) ∠A + ∠B

(b) ∠A + ∠C

(c) ∠B + ∠D

(d) ∠C + ∠D

Is it possible to have a regular polygon with a measure of each exterior angle as 22º.

(a) Yes

(b) No

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The no. of pairs of opposite angles of a quadrilateral is _____.

(a) 3

(b) 2

(c) 1

(d) 4

How many sides have a regular polygon, each angle of which is of measure 108º?

(a) 6 sides

(b) 3 sides

(c) 4 sides

(d) 5 sides

In the figure, ABCD is a trapezium in which AB = 7 cm, AD = BC = 5 cm, DC = x cm, and the distance between AB and DC is 4 cm. Find the value of x.

(a) 12 cm

(b) 15 cm

(c) 13 cm

(d) none of these

The diagonals do not necessarily intersect at right angles in a

(a) parallelogram

(b) rectangle

(c) rhombus

(d) kite

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What is the maximum exterior angle possible for a regular polygon?

(a) 120^{o}

(b) 90^{o}

(c) 130^{o}

(d) 85^{o}

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.

(a) 12

(b) 13

(c) 14

(d) 15

In the given figure, If x = ⅗ y and y = 5/7 z then the values of x, y and z are

(a) 60°,84°,36°

(b) 36°,84°,60°

(c) 36°,60°,84°

(d) 84°,60°,36°

All kites are rhombuses. True or False?

(a) True

(b) False

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Three angles of a quadrilateral are 30º, 150º and 100º. Find the fourth angle.

(a) 90^{o}

(b) 70^{o}

(c) 30^{o}

(d) 80^{o}

The sides of a pentagon are produced in order and the exterior angles so obtained are of measure *x*°, (2*x*°), (3*x* + 10)°, (4*x* + 5)° and (5*x*°) respectively. Find the value of *x*

(a) 22

(b) 19

(c) 23

(d) 25

In the adjoining figure, if ABCD is a square, the value of x is

(a) 45°

(b) 60°

(c) 70°

(d) 30°

Two adjacent angles of a parallelogram are equal. Find the measure of each angle of the parallelogram.

(a) 90^{o}

(b) 80^{o}

(c) 60^{o}

(d) 70^{o}

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A quadrilateral has all four angles of the same measure. What is the measure of each?

(a) 60°

(b) 70°

(c) 80°

(d) 90°

Find the number of sides of a regular polygon, when each of its angles has a measure of 150°?

(a) 9

(b) 10

(c) 11

(d) 12

In the adjoining figure, ABCD is a parallelogram. If AB = 2AD and P is the mid-point of AB, then ∠CPD is equal to

(a) 60°

(b) 90°

(c) 45°

(d) 120°

If each interior angle of a regular polygon is 150º, how many sides does this polygon have?

(a) 12

(b) 9

(c) 10

(d) 11

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Find the length of the diagonal of a rectangle whose sides are 5 cm and 12 cm.

(a) 12 cm

(b) 13 cm

(c) 14 cm

(d) 15 cm

Two angles of a quadrilateral are of measure 80º each. The other two angles are also equal. What is the measure of either of these two angles?

(a) 70°

(b) 80°

(c) 90°

(d) 100°

The number of degrees at each exterior angle of a regular pentagon is

(a) 82º

(b) 60º

(c) 72º

(d) none of these

RENT is a rectangle. Its diagonals meet at *O*. Find *x*, if *OR* = 3*x* + 5 and *OT *= 2*x* + 7.

(a) 1

(b) 2

(c) 8

(d) 5

What is the measure of each angle of a regular hexagon?

(a) 125^{o}

(b) 120^{o}

(c) 110^{o}

(d) 90^{o}

If the diagonals of a quadrilateral are perpendicular to each other, it is always a square. True or False?

(a) True

(b) False

The interior angle of a regular polygon is 156º. The number of sides of the polygon is

(a) 15

(b) 12

(c) 18

(d) none of these

Identity of all quadrilaterals that have four right angles

(a) Square and rectangle

(b) Square and rhombus

The ratio between the exterior angle and the interior angle of a regular polygon is 2 : 7. Find the number of sides in the polygon.

(a) 8 sides

(b) 9 sides

(c) 10 sides

(d) 11 sides

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The two diagonals are not necessarily equal in a

(a) rectangle

(b) square

(c) rhombus

(d) isosceles trapezium

How many sides does a regular polygon have if the measure of an exterior angle is 36°.

(a) 7

(b) 8

(c) 9

(d) 10