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Question 1 : In a parallelogram ABCD, write the sum of angles A and B.

In parallelogram ABCD, Adjacent angles of a parallelogram are supplementary.
Therefore, ∠A + ∠B = 1800

Question 2 : In a parallelogram ABCD, if ∠D = 1150, then write the measure of ∠A.

In a parallelogramABCD,

D = 1150 (Given)

Since, A and D are adjacent angles of parallelogram.

We know, Adjacentangles of a parallelogram are supplementary.

A + D = 1800

A = 180–115= 650

Measure of A is 650.

Question 3 : PQRS is a square such that PR and SQ intersect at O. State the measure of ∠POQ.

PQRS is a square suchthat PR and SQ intersect at O. (Given)

We know, diagonals ofa square bisects each other at 90 degrees.

So, POQ = 900

Question 4 : In a quadrilateral ABCD, bisectors of angles A and B intersect at O such that ∠AOB = 75°, then write the value of ∠C + ∠D.

AOB = 75o (given)

In a quadrilateralABCD, bisectors of angles A and B intersect at O, then

AOB = 1/2 (ADC + ABC)

or AOB = 1/2 (D + C)

By substituting givenvalues, we get

75 o =1/2 (D + C)

or C + D = 150 o

Question 5 :

The diagonals of a rectangle ABCD meet at O. If BOC = 44o, find OAD.

ABCD is a rectangleand BOC = 44o (given)

AOD = BOC (vertically opposite angles)

AOD = BOC = 44o

OAD = ODA (Angles facing same side)

and OD = OA

Since sum of all theangles of a triangle is 180 o, then

So, OAD = 1/2 (180 o – 44 o)= 68 o

Question 6 :

If PQRS is a square, then write the measure of SRP.

PQRS is a square.

All side are equal,and each angle is 90o degrees and diagonals bisect the angles.

So, SRP = 1/2 (90 o) = 45o

Question 7 :

If ABCD is a rectangle with BAC = 32o,find the measure of DBC.

ABCD is a rectangleand BAC=32 o (given)

We know, diagonals ofa rectangle bisects each other.

AO = BO

DBA = BAC = 32 o (Angles facing same side)

Each angle of arectangle = 90 degrees

So, DBC + DBA = 90 o

or DBC + 32 o = 90 o

or DBC = 58 o

Question 8 :

If ABCD is a rhombus with ABC = 56o,find the measure of ACD.

In a rhombus ABCD,

o

So,

or

We know, consecutiveangles of a rhombus are supplementary.

BCD + ABC = 180 o

BCD = 180 o – 56 o = 124 o

Equation (1)  o = 62 o

Question 9 :

The perimeter of a parallelogram is 22 cm. If the longer side measure 6.5cm, what is the measure of shorter side?

Perimeter of aparallelogram = 22 cm. (Given)

Longer side = 6.5 cm

Let x be the shorterside.

Perimeter = 2x + 2×6.5

22 = 2x + 13

2x = 22 – 13 = 9

or x = 4.5

Measure of shorterside is 4.5 cm.

Question 10 : If the angles of a quadrilateral are in the ratio 3:5:9:13, then find the measure of the smallest angle.

Angles of aquadrilateral are in the ratio 3 : 5 : 9 : 13 (Given)

Let the sides are 3x,5x, 9x, 13x

We know, sum of allthe angles of a quadrilateral = 360o

3x + 5x + 9x + 13x =360 o

30 x = 360 o

x = 12 o

Measure of smallestangle = 3x = 3(12) = 36o .

Todays Deals  ### RD Chapter 14- Quadrilaterals Ex-VSAQS Contributors krishan

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