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RD Chapter 8- Lines and Angles Ex-8.3 Interview Questions Answers

Question 1 : In figure, lines l1, and l2 intersect at O, formingangles as shown in the figure. If x = 45. Find the values of y, z and u.

Answer 1 :

Given: x = 450

Since vertically opposite angles are equal, therefore z = x = 450

z and u are angles that are a linear pair, therefore, z + u =1800

Solve, z + u = 1800 , for u

u = 1800 – z

u = 1800 – 45

u = 1350

Again, x and y angles are a linear pair.

x+ y = 1800

y = 1800 – x

y =1800 – 450

y = 1350

Hence, remaining angles are y = 1350, u = 1350 andz = 450.

Question 2 :

In figure, threecoplanar lines intersect at a point O, forming angles as shown in the figure.Find the values of x, y, z and u .

Answer 2 :

(BOD,z); (DOF, y) are pair of vertically opposite angles.

So, BOD = z= 900

DOF = y= 500

[Vertically oppositeangles are equal.]

Now, x + y + z = 180 [Linear pair] [AB is a straight line]

x + y + z = 180

x + 50 + 90 = 180

x = 180 – 140

x = 40

Hence values of x, y, z and u are 400, 500,900 and 400 respectively.

Question 3 : In figure, find the values of x, y and z.

Answer 3 :

From figure,

y = 250 [Vertically opposite angles are equal]

Now x + y = 1800 [Linear pair ofangles]

x = 180 – 25

x = 155

Also, z = x = 155 [Vertically opposite angles]

Answer: y = 250 and z = 1550

Question 4 :

In figure, find thevalue of x.

Answer 4 :

AOE = BOF = 5x [Vertically opposite angles]

COA+AOE+EOD = 1800 [Linear pair]

3x + 5x + 2x = 180

10x = 180

x = 180/10

x = 18

The value of x = 180

Question 5 :

Prove thatbisectors of a pair of vertically opposite angles are in the same straightline.


Answer 5 :


Lines AB and CD intersect at point O, such that

AOC = BOD (vertically angles) …(1)

Also OP is the bisector of AOC and OQ is the bisector of BOD

To Prove: POQ is a straight line.

OP is the bisector of AOC:

AOP = COP …(2)

OQ is the bisector of BOD:

BOQ = QOD …(3)

Now,

Sum of the angles around a point is 360o.

AOC + BOD + AOP + COP + BOQ + QOD = 3600

BOQ + QOD + DOA + AOP + POC + COB = 3600

2QOD + 2DOA + 2AOP = 3600 (Using (1), (2) and (3))

QOD + DOA + AOP = 1800

POQ = 1800

Which shows that, the bisectors of pair of vertically oppositeangles are on the same straight line.

Hence Proved.

Question 6 :

If two straightlines intersect each other, prove that the ray opposite to the bisector of oneof the angles thus formed bisects the vertically opposite angle.

Answer 6 :

Given AB and CD are straight lines which intersect at O.

OP is the bisector of  AOC.

To Prove : OQ is the bisector of BOD

Proof :

AB, CD and PQ are straight lines which intersect in O.

Vertically opposite angles: AOP =  BOQ

Vertically opposite angles: COP =  DOQ

OP is the bisector of  AOC :  AOP=  COP

Therefore,  BOQ =  DOQ

Hence, OQ is the bisector of BOD.


Selected

 

RD Chapter 8- Lines and Angles Ex-8.3 Contributors

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