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16. Since, the ratio of its internal to external angle is 7:2, you can say that
its internal angle = 7x and exterior angle = 2x.
Therefore,
7x + 2x = 180
=> x = 20
Exterior angle = 40 degrees
now (exterior angle) = 360/(no. of sides)
solving, you will get no. of sides = 9.
17. In paralelogram opposite sides are equal .
26 = 3y - 1
26 +1 = 3y
27 = 3y
27\3 + y
9 = y
18 = 3x
18\3 = x
6 = x.
18. The number of sides of a polygon with each exterior angle 60∘ is 6.
19. let the quad ABCD with angles in ratio 3:4:5:6
let the angles be 3x,4x,5x,6x
3x+4x+5x+6x=360° (angle sum property of quad.)
18x=360°
x=20
therefore, the angles are
3x=3·20=60°-A
4x=4·20=80°-B
5x=5·20=100°-C
6x=6·20=120°-D
now,A and D are supplementary
and,B and C are supplementary
∴AB║CD
when 2 opposite sides are parallel, the quad. is trapezium.
20. ∠BOA = 90º (vertically opposite angle)
∠BA0 = 180 - 56 - 90 = 34º (Sum of angles in a triangle)
∠BCA = 56º (Isosceles triangle)
∠BAC = 180 - 56 - 56 = 68º (Sum of angles in a triangle)
∠CAB = ∠BAC - ∠BAO
∠CAB = 68 - 34 = 34º
Answer: ∠CAB = 34º.
21. ⇒ In the given figure ABCD is a rectangle.
⇒ OA=2x+4 and OD=3x+1 [Given]
⇒ AC and BD are diagonals of a rectangle.
⇒ We know that diagonals of a rectangle are equal.
⇒ So, AC = BD
We can also write it as,
⇒ 2×OA=2×OD
⇒ 2×(2x+4) =2×(3x+1)
⇒ 2x+4=3x+1
∴ x=3
22. Let ABCD is a rhombus.
⇒ AB=BC=CD=DA [ Adjacent sides are eqaul in rhombus ]
In △AOD and △COD
⇒ OA=OC [ Diagonals of rhombus bisect each other ]
⇒ OD=OD [ Common side ]
⇒ AD=CD
∴ △AOD≅△COD [ By SSS congruence rule ]
⇒ ∠AOD=∠COD [ CPCT ]
⇒ ∠AOD+∠COD=180
[ Linear pair ]
⇒ 2∠AOD=180
∴ ∠AOD=90
23. we know that sum of adjacent angle in a parallelogram is 180.
3x-4+3x+10=180
6x+6=180
6x=180-6
x=174/6
x=29
therefor 1st angle=3*29-4=83
2nd angle=3*29+10=97
24. angle A + angle B + angle C + angle D = 360°
100° + angle B + angle C + angle D = 360°
angle B + angle C + angle D = 360° - 100°
angle B + angle C + angle D = 260°
4 + 6 + 3 = 260°
13 = 260°
(1) 13. 260°
4 ?
260×4/13= 80°
(2) 13 260°
6 ?
260×6/13= 120°
(3)13 260°
3 . ?
260×3/13= 60°
25. Let ABCD be the parallelogram.
Now, AB = 4.8 cmBC = 32AB = 32×4.8 = 7.2 cm
Now, CD = AB = 4.8 cm (opposite sides of ∥gm are equal)
AD = BC = 7.2 cm (opposite sides of ∥gm are equal)
Now, perimeter = AB + BC + CD + DA = 4.8 + 7.2 + 4.8 + 7.2 =24 cm.
26. let the other two angles be 2x and 3x.
Sum of angles of a quad.=360
160+2x+3x=360
5x=360-160
x=200/5
x=40
2x=2×40=80
3x=3×40=120.
27. If you know that the diagonal (hypotenuse) of the rectangle is 5 cm, and one of the sides is 3 cm, you can calculate the length of the other side using the Pythagorean theorem.
(c2 = a2 + b2)
5^2 = 3^2 + b^2
25 = 9 + b^2
16 = b^2
b = sqrt (16) = 4 cm
Since the perimeter of a rectangle = 2w + 2l, P = 2(3) + 2(4) = 14 cm.
28. Given that
ABCD is a Parallelogram.
and
∠EBA = 110°
∠EBA and ∠ABC are linear pair.
∠EBA + ∠ABC = 180°
=> 110° + Z = 180°
=> Z = 180° - 110°
=> Z = 70°
The value of Z = 70°
and
We know that
In a Parallelogram
Opposite angles are equal.
∠ABC = ∠CDA
=> Z = P
=> P = 70°
The value of P = 70°
and we know that
Adjacent angles are supplementary in a Parallelogram
∠CDA + ∠DAB = 180°
=> 70° + Y = 180°
=> Y = 180°-70°
=> Y = 110°
The value of Y = 110°
In a Parallelogram
Opposite angles are equal.
Y =X
X = 110°
The value of X = 110°
Answer:-
The value of X = 110°
The value of Y = 110°
The value of P = 70°
The value of Z = 70°
29. Given :-
diagonal of rhombus = 6cm
second diagonal = 8cm
perimeter = ?
we will use Pythagoras theorem
AC² = AB² + BC²
AC² = 6² +8²
AC² = 36 +64
AC² = 100
AC =√100
AC = 10 cm
perimeter of rhombus = 4* side
but it's half of diagonal
perimeter = 2*10 = 20cm.
30. consider angle DAB=angle 1 =120
angle ABC=angle 2=80
angle BCD=angle 3=60
angle CDA =angle 4=m
to find m
in a quad abcd sum of interior angles =360
1 +2+3+4=180
120+80+60+m=360
m=360-260
m=100
x+angle 1 =180(linear pair)
x+120=180
x=180-120=60
y+angle 2 =180(linear pair)
y+80=180
y=180-80=100
z+angle 3 =180(linear pair)
z+60=180
z=180-60=120
w+angle4 =180(linear pair)
w+100=180
w=180-100=80
Total =w+x+y+z
60+100+120+80=360
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