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

 Exercise 9F

Question 1

l||m, Find ∠a, ∠b, ∠c and ∠d in the same order.

Sol :

∠a=(180°-108°)=72°

∴∠b=72° (corresponding ∠s)

∴∠c=(180°-108°)=72°

∴∠d=(180°-72°)=108°

Question 2

Find each of the lettered angles giving reasons

(a) 

Sol :

∠a=(180°-85°)=95°

∴∠b=∠c=95°

(b)

∠x=135°  (corresponding ∠s)

∠x+∠y+90°=360°

∴∠y=360°-(90°+135°)

=360°-225°=135°

(c)

<fig to be added>

∴∠b=180°-120°=60° (co-interior ∠s)

∴∠a=45° (corresponding ∠s)

∠c₁=45°

∠b₁=180°-60°=120°

∠c-∠c₁=180°-120°=60°

∴∠c=60°+45°=105°

Question 3

Sol :

<fig to be added>

(a) 

∠x=∠y (corresponding ∠s AB||IJ)

∠y₁=180°-3x (co-interior ∠s)

180°-∠3x+∠x=86°

-∠2x=-94°

∠x$=\frac{94^{\circ}}{2}$

∴∠x=47°

<fig to be added>

(b) 

o₁=x (corresponding ∠s)

o₂=2x (corresponding ∠s)

x+2x=201°

3x=201°

$x=\frac{201^{\circ}}{3}=67°$

Fig to be added

(c)

∠1=180°-100°=80° (co-interior ∠s)

∠2=180°-115°=65° (co-interior ∠s)

∴∠1+∠a+∠2=180°

80°+∠a+65°=180°

∠a=180°-(80°+65°)=180°-145°=35°

fig to be added

(d)

Draw P||AB and DE

∠B=c₁=34° (corresponding ∠s, AB||P)

∠CDE=360°-226°=134°

∠c₂=180°-134°=46° (co-interior ∠s)

∠c₁+∠c₂=∠c

34°+46°=x+15°

x+15°=80°

x=80°-15°=65°

fig to be added

(e)

Draw P||AB and DE

∠B=360°-194°=166°

∠c₁=180°-166°=14°

∠c₂=63°-14°=49°

∴∠c₁=∠D=x=49°

fig to be added

(f)

Draw CF||AB||DE

∠c₁=28° (corresponding ∠s, CF||AB)

∠D₁=360°-249°=111°

∠c₂=180°-111°=69° (co-interior ∠s)

28°+69°=2x+13°

2x=97°-13°=84°

$x=\frac{84}{2}$=42°