#### Chapter 8 Lines and Angle R.D. Sharma Solutions for Class 9th Math MCQ

**Multiple Choice Questions**

(a) 130Â°

(b) 135Â°

(c) 90Â°

(d) 120Â°

**Solution**

(a) 45Â°

(b) 30Â°

(c) 36Â°

(d) none of these

**Solution**

3. Two straight line AB and CD intersect one another at the point O. If âˆ AOC + âˆ COB + âˆ BOD = 274Â°, then âˆ AOD =

(i) 86Â°

(ii) 90Â°

(iii) 94Â°

(iv) 137Â°

**Solution**

4. Two straight lines AB and CD cut each other at O. If âˆ BOD = 63Â°, then âˆ BOC =

(a) 63Â°

(b) 117Â°

(c) 17Â°

(d) 153Â°

**Solution**

5. Consider the following statements:

When two straight lines intersect:

(i) adjacent angles are complementary

(ii) adjacent angles are supplementary

(iii) opposite angles are equal

(iv) opposite angles are supplementary

Of these statements

(a) (i) and (ii) are correct

(b) (ii) and (iii) are correct

(c) (i) and (iv) are correct

(d) (ii) and (iv)Â are correct

**Solution**

Let us draw the following diagram showing two straight lines AD and BC intersecting each other at a point O.

(i) When two lines intersect adjacent angles are complementary.

This statement isÂ

__incorrect__

Explanation:

As the adjacent angles form a linear pair and they are supplementary.

Â (ii) When two lines intersect adjacent angles are supplementary.

This statement isÂ

__correct.__

Explanation:

As the adjacent angles form a linear pair and they are supplementary.

(iii) When two lines intersect opposite angles are equal.

This statement isÂ

__correct.__

Explanation:

As the vertically opposite angles are equal.

(iv) When two lines intersect opposite angles are supplementary.

This statement isÂ

__incorrect.__

Explanation:

As the vertically opposite angles are equal

Thus, out of all, (ii) and (iii) are correct.

Hence, the correct choice is (b).

6. Given âˆ POR = 3x and âˆ QOR = 2x + 10Â°. If POQ is a straight line, then the value of x is

(a) 30Â°

(b) 34Â°

(c) 36Â°

(d) none of these

**Solution**

*AOB*Â is a straight line. If âˆ

*AOC*Â + âˆ

*BOD*Â = 85Â°, then âˆ

*COD*Â =

(a) 85Â°

(b) 90Â°

(c) 95Â°

(d) 100Â°

**Solution**

8. In Fig. 8.123, the value ofÂ

*y*Â is

(a) 20Â°

(b) 30Â°

(c) 45Â°

(d) 60Â°

**Solution**Â

9. In Fig. 8.124, if y/x = 5 and z/x = 4, then the value of x is

(a) 8

(b) 18

(c) 12

(d) 15

**Solution**

10. In Fig. 8.125, the value ofÂ

(a) 12*x*Â is(b) 15

(c) 20

(d) 30

Â

**SolutionÂ**

11. In Fig. 8.126, which of the following statements must be true?

(i)Â

*a*Â +Â

*b*Â =Â

*d*Â +Â

*c*

(ii)Â

*a*Â +Â

*c*Â +Â

*e*Â = 180Â°

(iii)Â

*b*Â +Â

*f*Â =Â

*c*Â +Â

*e*

(a) (i) only

(b) (ii) only

(c) (iii) only

(d) (ii) and (iii) only

**Solution**

(i)Â Statement: a+b = d+c

This statement is incorrect.

Explanation: We have, a and dare vertically opposite angles.

Therefore, a=d ---(i)Â

Similarly, band e are vertically opposite angles.Â

Therefore,Â

b=e ---(ii)

On adding (i) and (ii), we getÂ

a+b=d+eÂ

Thus, this statement is incorrect.

(ii)Â Statement a+c+e = 180Â°Â

This statement is correct.

Explanation: As aÂ°, fÂ° and eÂ° form a linear pair, therefore their sum must be supplementary.

a+f+e = 180Â° ---(iii)

Also fÂ° and cÂ° are vertically opposite angles, therefore, these must be equal.

f =cÂ

Putting f=c in (iii), we get:

a+c+e=180Â°

(iii) Statement: b+ f =a+eÂ

This statement is correct.

Explanation:Â As aÂ°, fÂ° and bÂ° form a linear pair, therefore their sum must be supplementary.

a+ f +b=180Â° ---(iv)Â

Also cÂ°,dÂ° and eÂ° form a linear pair, therefore their sum must be supplementary.

c+d+e=180Â° ---(v)

On comparing (iv) and (v), we get:

a+ f +b=c+d+e

Also aÂ° and dÂ° are vertically opposite angles, therefore, these must be equal.

Therefore,

a= d

Substituting the above equation in (vi), we get:

a+f+b = c+d+eÂ

a+b+f = c+a+e

b+f = a+e

Thus, out of all, (ii) and (iii) are correct.

12. If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3, then the measure of the larger angle is

(a) 54Â°(b) 120Â°

(c) 108Â°

(d) 136Â°

**Solution**Â

(a) 85Â°

(b) 135Â°

(c) 145Â°

(d) 215Â°

**Solution**

14. In Fig. 8.128, ifÂ

*AB*Â ||Â

*CD*, then the value of

*Â x*Â is

(a) 20Â°

(b) 30Â°

(c) 45Â°

(d) 60Â°

**Solution**

15. AB and CD are two parallel lines. PQ cuts AB and CD at E and F respectively. EL is the bisector of âˆ FEB. If âˆ LEB = 35Â°, then âˆ CFQ will be

(a) 55Â°

(b) 70Â°

(c) 110Â°

(d) 130Â°

**Solution**

16. Two lines AB and CD intersect at O. If âˆ AOC + âˆ COB + âˆ BOD = 270Â°, then âˆ AOC =

(a) 70Â°

(b) 80Â°

(c) 90Â°

(d) 180Â°

**Solution**

17. In Fig. 8.129, PQ || RS, âˆ AEF = 95Â°, âˆ BHS = 110Â° and âˆ ABC = xÂ°. Then the value of x is

(a) 15Â°

(b) 25Â°

(c) 70Â°

(d) 35Â°

**Solution**

Â

Â

**SolutionÂ**19. In Fig. 8.131, if l1âˆ¥l2, what is x+y in terms of w and z?

(a) 180-w+z

(b) 180+w-z

(c) 180-w-z

(d) 180+w+z

**Solution**

20. In Fig. 8.132, if l1âˆ¥l2, what is the value of y?

(a) 100

(b) 120

(c) 135

(d) 150

**Solution**

21. In Fig. 8.133, if l1âˆ¥l2 and l3âˆ¥l4, what is y in terms of x?

(a) 90+x

(b) 90+2x

(c) 90 - x/2

(d) 90-2x

**Solution**

22. In Fig. 8.13, if lâˆ¥m, what is the value of x?

(b) 50

(c) 45

(d) 30

**Solution**

23. In Fig. 8.135, if the line segment AB is parallel to the line segment CD, what is the value of y?

(a) 12

(b) 15

(c) 18

(d) 20

**Solution**

(a) 130Â°

(b) 105Â°

(c) 175Â°

(d) 125Â°

**Solution**

25. In Fig. 8.137, if AB || HF and DE || FG, then the measure of âˆ FDE is

(a) 108Â°

(b) 80Â°

(c) 100Â°

(d) 90Â°

**Solution**

26. In Fig. 8.138, if lines l and m are parallel then x =

(a) 20Â°

(b) 45Â°

(c) 65Â°

**Solution**

27. In Fig. 8.139, if ABâˆ¥CD, then x =

(a) 100Â°

(b) 105Â°

(c) 110Â°

(d) 115Â°

**Solution**

28. In Fig. 8.140, if lines l and m are parallel lines, then x =

(a) 70Â°

(b) 100Â°

(c) 40Â°

(d) 30Â°

**Solution**

29. In Fig. 8.141, if lâˆ¥m, then x =

(a) 105Â°

(b) 65Â°

(c) 40Â°

(d) 25Â°

**Solution**

30. In Fig. 8.142, if lines l and m are parallel, then the value of x is

(a) 35Â°

(b) 55Â°

(c) 65Â°

(d) 75Â°

**Solution**