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QUESTION: 1

In a parallelogram ABCD, if ∠A = 115°, then ∠B, ∠C and ∠D are

Solution:

In a parallelogram ABCD, ∠D = 115° (Given)

Since, ∠A and ∠D are adjacent angles of parallelogram.

We know, Adjacent angles of a parallelogram are supplementary.

∠A + ∠D = 180°

∠A = 180° – 115° = 65°

Measure of ∠A is 65°.

QUESTION: 2

Choose the correct statement

Solution:

QUESTION: 3

Which of the following is not a parallelogram?

Solution:

QUESTION: 4

In the figure ABCD is a ||^{gm} in which ∠DAB = 80° and ∠DBC = 60°, then ∠CDB and ∠ADB are equal to

Solution:

QUESTION: 5

A quadrilateral is a ______ if a pair of opposite sides is equal and parallel

Solution:
Parallelogram because it have pair of opposite sides are equal and parallel

QUESTION: 6

If every pair of adjacent sides of a quadrilateral are equal, then the quadrilateral is a

Solution:

QUESTION: 7

In a parallelogram ABCD, if ∠A = 60°, then ∠D is equal to:

Solution:

QUESTION: 8

Each diagonal of a parallelogram divides it into two

Solution:

QUESTION: 9

Statement 1: AB||DC and AD||BC

Statement 2: AB = DC and AD=BCFor a quadrilateral ABCD to be a parallelogram,__________

Solution:

QUESTION: 10

Perimeter of a parallelogram is 22 cm. If the longer side, measures 6.5 cm, the measure of the shorter side will be:

Solution:

Let the length of the shorter side be x cm

length of longer side= 6.5 cm

perimeter= 22 cm

>2[sum of adjacent sides]=22

>2[longer side+shorter side]=22

>2[6.5+x] = 22 = 22/2 =11

>6.5 + x =11 = 11 - 6.5 = 4.5

> x= 4.5

QUESTION: 11

In the figure ABCD is a square. A line segment DX cuts the side BC at X and the diagonal AC at O such that ∠COD = 105° and ∠OXC = y. Then y is equal to

Solution:

Given :In the figure ABCD is a square. A line segment DX cuts the side BC at X and the diagonal AC at O such that COD = 105 degree and OXC = y

To find :y

Since DX is a line segment, then

angle COD + angle COX = 180 degrees {Angle sum property}

=> angle COX = 180 -105 = 75 degrees..(1)

Since ABCD is a square and AC is a diagonal , therefore all the angles in a square is 90 degree each and AC bisects the angle in half. {property}

=> angle ACB { also OCX } = 90 /2 =45 degrees...(2)

In traingle COX

=> angle OCX + angle COX + y = 180 degree { sum of angles in a triangle is 180 degree}

=> y = 180 - (45+75) {using eq 1 and 2}

=> y = 60 degrees Answer

QUESTION: 12

Which of the following is not true for a parallelogram?

Solution:

QUESTION: 13

In a parallelogram, if ∠A = (2x +25)° and ∠B = (3x – 5)°, the value of x is

Solution:

QUESTION: 14

If an angle of a parallelogram is four-fifths of the adjacent angle, then the angles of the parallelogram are

Solution:

QUESTION: 15

In fig., PQRS is a parallelogram in which ∠PSR = 125°, ∠RQT is equal to

Solution:

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