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Ncrt math
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Summary of 28 pages for the course Mathematic at (Ncrt math book)
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Class IX Chapter 14 – Quadrilaterals Maths______________________________________________________________________________
Exercise – 14.1
1. Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth
angles.
Sol:
Given
Three angles are 110,50 and 40
Let fourth angle be 𝑥
We have,
Sum of all angles of a quadrilaterals 360
110 50 40 x 360
x 360 200
x 160
Required fourth angle 160 .
2. In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure
of each angles of the quadrilateral.
Sol:
Let the angles of the quadrilateral be
A x, B 2 x, C 4 x and D 5x then,
A B C D 360
x 2x 4x 5x 360
12x 360
360
x
12
x 30
A x 30
B 2 x 60
C 4 x 30 4 120
D 5 x 5 30 150
3. In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that
1
∠COD = 2 (∠𝐴 + ∠𝐵).
Sol:
In DOC
1 COD 2 180 [Angle sum property of a triangle]
COD 180 1 2
COD 180 1 2
,Class IX Chapter 14 – Quadrilaterals Maths
______________________________________________________________________________
1 1
COD 180 C D
2 2
[ OC and OD are bisectors of C and D represents]
1
COD 180 C D ..... 1
2
In quadrilateral ABCD
A B C D 360
C D 360 A B ...... 2 [Angle sum property of quadrilateral]
Substituting (ii) in (i)
COD 180 360 A B
1
2
1
COD 180 180 A B
2
1
COD A B
2
4. The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
Sol:
Let the common ratio between the angle is ‘𝑥’ so the angles will be 3x,5 x,9 x and 13x
respectively
Since the sum of all interior angles of a quadrilateral is 360
3x 5x 9x 13x 360
30x 360
x 12
Hence, the angles are
3x 312 36
5x 5 12 60
9 x 9 12 108
13x 1312 156
, Class IX Chapter 14 – Quadrilaterals Maths
______________________________________________________________________________
Exercise – 14.2
1. Two opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each
angle of the parallelogram.
Sol:
We know that
Opposite sides of a parallelogram are equal
3x 2 50 x
3x x 50 2
4 x 52
x 13
3 x 2 3 13 2 37
50 x 50 13 37
Adjacent angles of a parallelogram are supplementary
x 37 180
x 180 37 143
Hence, four angles are : 37,143,37,143
2. If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the
parallelogram.
Sol:
Let the measure of the angle be x
2x
The measure of the angle adjacent is
3
We know that the adjacent angle of a parallelogram is supplementary
2x
Hence x 180
3
2x 3x 540
5x 540
x 108
Adjacent angles are supplementary
x 108 180
x 180 108 72
x 72
Hence, four angles are : 180, 72,108, 72
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