# 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.

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