# In the given figure l||m and t is a transversal. If angle 2 and 1 are in the ratio 5 and 7 ,find the measure of each of the angles 1 2 3 and 8.

As we know that angle 1 and 2 form a linear pair,
Therefore angle 1+2 = 180 degree

Therefore if we take the the base of each angle = x
Therefore their ratio = 5x:7x
​Therefore 5x+7x = 180 degree
​12x = 180 degree
x = 180/12 degree
x =15

Therefore angle 1 = 15*5 = 75 degree
Therefore angle 2 = 15*7 = 105 degree

As we know angle 2 and 3 are also forming a linear pair,
Therefore angle 2+3 = 180 degree
105+(angle 3) = 180 degree
angle 3 = 75 degree

Now we also get angle 3 and 4 as a linear pair,
Therefore angle 3+4 = 180 degree
75+(angle 4) = 180 degree
angle 4 = 105 degree

As we know that angle 4 and 8 are coresponding angle,which are equal,
Therefore angle 8 = 105 degree

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1= 105
2= 75
3= 105
8=75
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In the figure l parallel to M and transversal t intersects at a and b and one is 2 angle 2 equals to 11 is to 7 determine all the 8 angles
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Thank😊😊😊

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ANS     1=150
2=75
3=105
8=75
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angle 1 and 2 form linear pair so,
let the angle be 5x and 7x
so, 5x + 7x = 180
12x = 180
x = 180/12
x = 15
now, angle one 7x = 7 X 15 = 105 degree
angle two  5x = 5 X 15 =  75   degree
now angle 3 = angle 1 , angle 4 = angle 2            ( vertically opposite angle are always same)
and  angle 8 = angle 4                                         (corresponding interior angle )

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