S.chand publication New Learning Composite mathematics solution of class 8 Chapter 10 Quadrilaterals Exercise 10A

 Exercise 10A

Find the value of unknown angle in each of the following figures.


Q1(a) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 1

(a) 75°+125°+105°+x=360°

305°+x=360°

x=360°-305°=55°



Q1(a) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 1(b)

(b) 80°+100°+70°+y=360°

y+250°=360°

y=360°-250°=110°



Q1(c) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 1(c)

(c) 90°+140°+30°+a=360°

a+260°=360°

a=360°-260°=100°



Q1(d) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 1(d)






Sol :

(d) ΔABC

∠CAB=(20°+z)

∠BCA=(10°+y)

∠ABC=40°

∴∠ABC+∠CAB+∠BCA=180°

40°+(20°+z)+(10°+y)=180°

(z+y)=180°-70°=110°


Now ΔAOC

∠CAO+∠ACO+∠AOC=180°

z+y+∠AOC=180°

110°+∠AOC=180°

∠AOC=180°-110°=70°

x=360°-70°=290°




Q1(e) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 1(e)









(e) p+70°+90°+90°=360°

p+250°=360°

p=360°-250°=110°




Q1(f) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 1(f)






(f) 138°+90°+x+2x=360°

288°+2x+x=360°

3x=360°-288°

3x=72°

$x=\frac{72}{3}=24^{\circ}$

∴2x=2×24=48°



Q1(g) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 1(g)

(g) m+2m+m+2m=360°







6m=360°

$m=\frac{360}{6}$=60°

∴∠A=60° ,∠B=2×60°=120°

∠C=60° ,∠D=2×60°=120°



Q1(h) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 1(h)






Sol :

(h) ∠O=360°-240° =120° 

∴ΔBOC⟶

∠BOC+∠OBC+∠OCB=180° 

,120°+a+b=180°

a+b=180°-120°=60°


Now , ΔABC⟶

∠ABC+∠ACB+∠BAC=180°

(y+a)+(30°+b)+65°=180°

y+(a+b)+30°+65°=180°

y+60°+30°+65°=180°

y=180°-155°=25°


Find the value of x


Q2(a) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 2(a)


(a) ∠BCD=180°-60°=120°

∴120°+110°+50°+x=360°

280°+x=360°

x=360°-280°=80°




Q2(b) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 2(b)







Sol :

(b) ∠EDF=∠ADC=35° (Vertically Opposite Angles)

∴90°+136°+35°+x=360°

x=360°-261°=99°



Q2(c) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 2(c)

(c) 3x+4x+2x+x=360°

10x=360°

$x=\frac{360}{10}$=36°

∴3x=3×36°=108°

4x=4×36°=144°

2x=2×36°=72°



Q2(d) | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 2(d)

(d) ∠DAB=90°

∠ABC=180-100=80°

∠DCB=x

∠CDA=180-70=110°

x+110+80+90=360°

x+280=360°

x=360°-280°=80°



Q3 | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 3

Find the measures of the four angles of a quadrilateral if they are in the ratio 2 : 4 : 6 : 8.

Sol :

Angle ratio=2 : 4 : 6 : 8

∴common factor=x

2x+4x+6x+8x=360°

20x=360°

$x=\frac{360}{20}$=18°

2x=2×18°=36°

4x=4×18°=72°

6x=6×18°=108°

8x=8×18°=144°



Q4 | Ex-10A | Class 8 | SChand New learning Composite Maths | Quadrilaterals | myhelper

OPEN IN YOUTUBE

Question 4

Find the value of x if x, (2x+13°), (3x+10°) and (x–6°) are all the angles of a quadrilateral?

Sol :

x+(2x+13°)+(3x+10°)+(x-6°)=360°

x+2x+3x+x+13°+10°-6°=360°

7x+17=360

7x=360°-17°=343°

$x=\frac{343}{7}$=49°

2x+13°=2×49°+13°=111°

3x+10°=3×49°+10°=157°

x–6°=49°-6°=43°


1 comment:

Contact Form

Name

Email *

Message *