S.chand publication New Learning Composite mathematics solution of class 7 Chapter 10 Properties of Triangles Exercise 10B

 Exercise 10B

Question 1

Name the interior opposite angles in the figure associated with the exterior angle.

(a) ACS

Sol : ∠ABC ,∠BAC

(b) RBA

Sol : ∠BAC, ∠ACB

(c) TAB

Sol : ∠ABC, ∠ACB

(d) QBC

Sol : ∠BAC, ∠ACB

(e) PAC

Sol : ∠ABC, ∠ACB

(f) BCU

Sol : ∠ABC, ∠BAC


Question 2

Find the unknown marked angle.

(a)

a=67°+38°=105°  [ext. ∠property of  a Δ]


(b) 

119°=46°+b [ext. ∠property of  a Δ]

b=119°-46°=73°


(c)

125°=59°+c  [ext. ∠property of  a Δ]

c=125°-59°=66°


(d)

88°=24°+a  [ext. ∠property of  a Δ]

a=88°-24°=64°


Question 3

Find ∠R

Fig to be added

(5x-2)°+(4x+15)°  [ext. ∠property of  a Δ]

5x-2°+4x+15°=130°

9x+13°=130°

9x=130°-13°=117°

$x=\frac{117}{9}$

∴x=13°

∠R=(4x+15)°

={(4×13)+15}°

={52+15)°=67°


Question 4

Find ∠ACD

Fig to be added

(7x-9)°=90°+(3x+5)°

7x-9-3x-5=90°

4x-14=90°

4x=90°-14°=104°

$x=\frac{104}{4}$

x=26°

∴∠ACD=(7x-9)°

={(7×26)-9}°

={182-9}°=173°


Question 5

Find the unknown marked angles, without using the angle sum property of  a triangle

(a) Fig to be added

a=62°+32°=94°  [ext. ∠property of a Δ]

b=180°-94°=86°

c=32°+86°=118°  [ext. ∠property of a Δ]


(b) Fig to be added

P=90°+43°=133°  [ext. ∠property of a Δ]

q=180°-133°=47°

r=180°-90°=90°


(c) Fig to be added

x=180°-(65°+48°)

=180°-113°=67°


v=67°  (corresponding ∠s AB||CD)


u=67°+65°=132°  [ext. ∠property of a Δ]


(d) Fig to be added

y=50°  (corresponding ∠s, AB||DE)

∴x=25°+50°=75°  [ext  ∠s property of a Δ]


Question 6

Find x, without using the property of angle sum property of a triangle. State your reasons clearly

(a) Fig to be added

y=5x  (corresponding ∠s, AB||DE)

4x+5x=72°  [ext  ∠s property of a Δ]

9x=72°

$x=\frac{72}{9}$

x=8°


(b) Fig to be added

∠ACD=180°-4x

2x+3x=180°-4x  [ext. ∠s property of a Δ]
2x+3x+4x=180°
9x=180°
$x=\frac{180}{9}$
x=20°

(c) Fig to be added

y=180°-108°=72°

7x=4x+72°  [ext. ∠s property of a Δ]
7x-4x=72°
3x=72°
$x=\frac{72}{3}$
x=24°

(d) Fig to be added

9x=90°+4x [ext. ∠s property of a Δ]
5x=90°
$x=\frac{90}{5}$
x=18°

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