EXERCISE 13.1
1 If two angles of a quadrilateral are 40° and 110° and the other two are in the ratio
3:4, find these angles.
2 If the angles of a quadrilateral, taken in order, are in the ratio 1:2:3:4, prove that
it is a trapezium
3 If an angle of a parallelogram is two-thirds of its adjacent angle, find the angles of the
parallelogram
4 (a) In figure (1) given below, ABCD is a parallelogram in which ZDAB = 70°,
ZDBC = 80°. Calculate angles CDB and ADB.
Rectilinear Figures
281
Answers
Answer:
ANSWER 1)-
Given 2 angles are in ratio = 3:4
40+110+3x+4x = 360
7x +150= 360
7x = 360-150
7x = 210
x = 30
so other angles are 90,120
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ANSWER 2)-
Let the coefficient of the following ratios be x.
we know that sum of angles of quadrilateral equals 360°.
So,
1x+2x+3x+4x = 360.
10x = 360°.
x = 36°.
First angle = 36°.
Second angle = 72°.
Third angle = 108°.
Fourth angle = 144°.
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ANSWER 3)-
Given-ABCD is a parallelogram
2/3of its adjencent angleis equal
To prove-All the andle of a parallelogram
Proof- we assume that X is2/3 of its angle Y
X=2/3y.......eqn1
It is also known that the adjacent side of a parallelogram are supplimentary.so the sum of adjencent angle is 180degree
X+Y=180degree......eqn2
put the value of X from equation 1in eqn2
2/3y+Y=180degree
(2/3+1)Y=180degree
( 5/3)y=180degree
Y=180*3/5
Y=540/5=180degree
now put this value in eqn2 to get value of X
X+108=180
X=72
Hence adjencent angle of the parallelogram are 72degree and 180 degree
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