S.chand publication New Learning Composite mathematics solution of class 7 Chapter 9 Pairs and Angles Exercise 9G

 Exercise 9G

Question 1

State whether each pair of lines are (a) parallel or (b) not parallel Give reasons

(a) Parallel, alternative ∠S equal

(b) Parallel, Co-interior ∠S supplementary.

(c) Not Parallel, Co-interior ∠S not supplementary.

(d) Parallel, Alternative ∠S equal.

(e) Not parallel, corr. ∠S not equal.

(f) Parallel, corr. ∠S equal.

(g) Not parallel, Alt ∠S not equal.

(h) Not parallel, corr. ∠S not equal.

Question 2

Name all pairs of parallel lines in there diagonals. Give reasons.

(a) AB ∥ DC and AD ∥ BC, co-int ∠S supplementary.

(b) AB ∥ CD, Alt ∠S equal, CD ∥ EF, Alt. ∠S equal.

(c) PQ ∥ RS, corr. ∠S equal, RS ∥ TU, corr. ∠S equal.

Question 3

Show that m||n if the angles have measurements given below. Give reasons

Sol :

Fig to be added

(a)

 x=14

∠3=8x-7° 

=112°-7°=105°

∠6=6x+21° 

=(6×14)+21°

=84°+21°=105°

∠1=∠4=180°-105°=75°

∴∠2=105°

∠5=∠8=180°-105°=75°

∴∠7=105°

Ans : m||n because alt. ∠s are equal

(b)

x=25

∠1=4x+3°

=(4×25)+3°

=100+3=103°

∠5=5x-22°

=125°-22°=103°

∠2=∠3=180°-103°=77°

∠4=103°

∠6=∠7=180°-103°=77°

∠8=103°

Ans : m||n because corresponding ∠s are equal

(c)

∠4=(2×30°)+15°

=60°+15°=75°

∠6=3x+15°

=(3×30°)+15°

=90°+15°=105°

∴∠2=∠3=180°-75°=105°

∴∠1=75°

∴∠5=∠8=180°-105°=75°

∴∠7=105°

Ans : m||n because sum of co-interior ∠s=180°

Question 4

Is AB||CD ? Give reasons for your answer

(a) fig to be added

∠B=(32°+47°)=79°

∠D=(35°+66°)=101°

∴∠B+∠D=79°+101°=180°

Ans : AB||CD because sum of co-int ∠s=180°

(b) fig to be added

∠ABC≠∠BCD

AB∦CD

Ans : AB and CD are not parallel because alt ∠s are not equal

(c) fig t- be added

∠DAP=180°-125°=55°

∴∠DAP=55°-20°=35°

∠ADC=40°

∠DAB≠∠ADC

Ans : Ab not parallel to CD because alt. ∠s are not equal