Exercise 9A
Question 1
What is measure of complement of 380
Sol : 90°-38°=52°
Question 2
What is measure of supplement of 170°
Sol : 180°-170°=10°
Question 3
Tell whether the angles shown below are complementary, supplementary or neither.
Sol :
(a) Complementary
(b) Supplementary
(c) Neither
(d) Neither
Question 4
For each angle in group A, find its complement in group B. (Example 20° and 70°)
A: 20°, 10°, 35°, 45°, 60°, 85°, 65°
B: 25°, 45°, 30°, 5°, 70°, 80°, 55°
Sol :
20° and 70°
10° and 80°
35° and 55°
45° and 45°
60° and 30°
85° and 5°
65° and 25°
Question 5
For each angle in group A, find its supplement in group B.
A: 140°, 70°, 179°, 165°, 55°, 45°, 80°
B: 100°, 15°, 125°, 110°, 1°, 40°, 135°
Sol :
140° and 40°
70° and 110°
179° and 1°
165° and 15°
55° and 125°
45° and 135°
80° and 100°
Question 6
Two complementary angles are in the ratio 7:8, find the angles.
Sol :
Let, the angles be 7x and 8x
7x+8x=90
15x=90
$x=\frac{90}{15}$
∴x=6
Complementary angles are 42 and 48
Question 7
Two supplementary angles are in the ratio 3:7, Find the angles.
Sol :
Let , the angles are 3x and 7x
3x+7x=180
10x=180
$x=\frac{180}{10}$
∴x=18
∴The angles are 54 and 126
Question 8
Tell whether the angles are only adjacent, adjacent and form a linear pair or not adjacent.
(a) ∠1 and ∠4
Sol : Adjacent and form linear pair
(b) ∠2 and ∠3
Sol : Adjacent and form a linear pair
(c) ∠3 and ∠4
Sol : Only adjacent
(d) ∠3 and ∠1
Sol : Not adjacent
Question 9
Find the measures of the lettered angles.
(a) 90°
(b) 180°-108°=72°
∴P=72°
(c) 180°-39°=141°
∴x=141°
(d) 7b+2b=180°
9b=180°
$b=\frac{180^{\circ}}{9}$
b=20°
∴7b=(7×20)=140°
∴2b=(2×20)=40°
(e) 180°-(62°+53°)
=180°-115°
y=65°
(f) b+b+b=180°
3b=180°
$b=\frac{180^{\circ}}{3}$
∴b=60°
(g) 139°+d=180°
∴d=180°-139°=41°
c+49°=180°
∴c=180°-49°=131°
(h) f+32°=90°
∴f=90°-32°=58°
65°+g=90°
g=90°-65°=25°
Question 10
Find
(a) b, if a=110°
b=360°-110°=250°
(b) b, if $a=1\frac{1}{4}$ rt ∠s
$a=1\frac{1}{4} \times 90 ^{\circ}$
$=\frac{5}{4} \times 90^{\circ}$
=112.5°
∵a+b=360° (sum of angles around a point)
∴b=360°-112.5°=247.5°
$=\frac{11}{4}$ right angle
$=2\frac{3}{4}$ rt ∠s
(c) a, if b=258°
a=360°-258°=102°
(d) b, if b-3a=40°
b-3a=40°
or b=40°+3a
b=360°-a
40°+3a=360°-a
3a+a=360°-40°
4a=320°
$a=\frac{320^{\circ}}{4}$
∴a=80°
∴b=360°-80°=280°
Question 11
Find the values of a,b,c and d
(a)
a=360°-(70°+60°)
=360°-130°=230°
(b)
b=360°-(125°+59°+110°)
=360°-294°=66°
(c)
4c+5c=180°
9c=180°
$c=\frac{180^{\circ}}{9}=20^{\circ}$
∴c=20°
4c=80°
5c=100°
(d)
3d+62°+62°+105°+47°=360°
3d=360°-(62°+62°+105°+47°)
3d=360°-276°
3d=84°
∴d=28°
Question 12
Name the pairs of vertical angles
Sol :
∠3 and ∠6
∠2 and ∠5
∠1 and ∠4
Question 13
How many pairs of vertical angles are in the diagram ?
Sol : 4
Question 14
Find the values of each variable.
(a) a=60°
(b) ∠a=∠c$=\frac{360^{\circ}-(25^{\circ}+25^{\circ})}{2}$
$=\frac{360^{\circ}-50^{\circ}}{2}=\frac{310^{\circ}}{2}$
=155°
(c) y=x
2y+y=180°
3y=180°
$y=\frac{180^{\circ}}{3}$
∴y=60°
(d)
p+76°=180° (Linear Pair)
p=180°-76°=104°
∠p=∠r=104° (Vertically Opposite Angles )
4q=76° (Vertically Opposite Angles )
$q=\frac{76}{4}$
q=19°
Question 15
In the diagram on the right, ∠1 = 50° and ∠2 = 84°, find the measures of ∠3, ∠4, ∠5 and ∠6.
Sol :
If ∠1 = 50° then, ∠4=50°
If ∠2 = 84° then ,∠5=84°
∴∠3+∠6=360°-(50°+50°+84°+84°)
=360°-268°=92°
∴∠3$=\frac{92^{\circ}}{2}$=46°
and ∠6=46°
Question 16
Find the angles in each of the following.
(a) The angles are supplementary and the larger is 20° less than 3 times the smaller.
Sol :
Let, the smaller angle be x
ATQ,
x+(3x-20°)=180°
4x-20°=180°
4x=180°+20°
$x=\frac{200^{\circ}}{4}=50^{\circ}$(b) The angles are complementary and the larger is 15° more than twice the smaller.
Sol :
Let , the smaller angle be x
ATQ,
x+(2x+15°)=90°
3x=90°-15°
3x=75°
$x=\frac{75}{3}=25$
∴The smaller angle=25°
The larger angle=(2×25°)+15°
=50°+15°=65°
(c) The angles are adjacent and form an angle of 120°. The larger is 20° less than 3 times the smaller.
Sol :
Let, the smaller angle be x
The larger angle be (3x-20°)
ATQ,
x+(3x-20°)=120°
4x=120°+20°
$x=\frac{140^{\circ}}{4}$
x=35°
∴The smaller angle=35°
The larger angle=(3×35°)-20°
=105°-20°=85°
(d) The angles are vertical and complementary.
Sol :
Let, the angle be x and y
ATQ,
x=y
∴x+y=90°
y+y=90°
2y=90°
y=45°
∴The vertical angles are 45° and 45°
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