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

 Exercise 9E

Question 1

Find the measure of each unknown angle. Give reasons

Sol :

(a)

60°+∠1=180° (same side int ∠s)

∠1=(180°-60°)=120°

(b)

80°+∠x=180° (same side int ∠s)

or ∠x=180°-80°=100°

(c)

∠P+125°=180° (same side int ∠s)

∠P=180°-125°=55°

(d) 

∠a=115° (vertically opposite angle)

∠a+∠b=180° (same side int ∠s)

115°+∠b=180°

∠b=180°-115°=65°

(e)

x+2x=180° (∠x= vertically opposite angles and same side int ∠s)

3x=180°

$x=\frac{180}{5}$

∴x=60°

2x=(x×60°)=120°

(f)

∠a+70°=180° (same side int ∠s)

∠a=180°-70°=110°

∠b+130°=180°

∠b=180°-130°=50°

∠c+60°=180° (same side int ∠s)

∠c=180°-60°=120°

Question 2

Sol :

(2x+12°)+5x=180° (same side int ∠s)

2x+12°+5x=180°

7x=180°-12°=168°

$x=\frac{168}{7}$=24°

∴∠CBQ=2x+12°

=(2×24°)+12°

=48°+12°=60°

Question 3

Sol :

(10x+5y)°+80°=180° (same side int ∠s)

10x+5y=180°-80°

10x+5y=100°...(i)

(15x+4y)+72°=180°

15x+4y=180°-72°

15x+4y=108°...(ii)

∴{(i)×3}-{(ii)×2}

$\begin{array}{r}30x+15y=300^{\circ}\\ 30x+8y=216^{\circ}\\ (-)\phantom{30x}(-)\phantom{8y}=(-)\phantom{216^{\circ}} \\ \hline 7y=84^{\circ}\end{array}$

$y=\frac{84^{\circ}}{7}$

=12°

∴10x+5y=100°

10x+(5×12)=100°

10x+60°=100°

$x=\frac{40}{100}$

∴x=4°

Ans : x=4°, y=12°

Question 4

Sol :

70°+x=180° (same side int ∠s)

x=(180°-70°)=110°

50°+y=180° (same side int ∠s)

∴y=180°-50°=130°