### MCQ on understanding Quadrilaterals:

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

(a) rectangle

(b) square

(c) rhombus

(d) all of these

**Question: **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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**Question: **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}

**Question: **The sum of angles of a quadrilateral is _____ right angles.

(a) four

(b) two

(c) one

(d) none of these

**Question: **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

**Question: **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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**Question: **The no. of pairs of opposite angles of a quadrilateral is _____.

(a) 3

(b) 2

(c) 1

(d) 4

**Question: **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

**Question: **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

**Question: **The diagonals do not necessarily intersect at right angles in a

(a) parallelogram

(b) rectangle

(c) rhombus

(d) kite

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

(a) 120^{o}

(b) 90^{o}

(c) 130^{o}

(d) 85^{o}

**Question: **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

**Question: **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°

**Question: **All kites are rhombuses. True or False?

(a) True

(b) False

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**Question: **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}

**Question: **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

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

(a) 45°

(b) 60°

(c) 70°

(d) 30°

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

(a) 60°

(b) 70°

(c) 80°

(d) 90°

**Question: **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

**Question: **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°

**Question: **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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**Question: **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

**Question: **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°

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

(a) 82º

(b) 60º

(c) 72º

(d) none of these

**Question: **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

**Question: **What is the measure of each angle of a regular hexagon?

(a) 125^{o}

(b) 120^{o}

(c) 110^{o}

(d) 90^{o}

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

(a) True

(b) False

**Question: **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

**Question: **Identity of all quadrilaterals that have four right angles

(a) Square and rectangle

(b) Square and rhombus

**Question: **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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**Question: **The two diagonals are not necessarily equal in a

(a) rectangle

(b) square

(c) rhombus

(d) isosceles trapezium

**Question: **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