Question

In the given figure, ABCD and LN is a transversal If angle APM=30°,angle MOC=55°
and angle CON=45°,then find the value of x and y.
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Answer 1

Answer:

On taking line L

Let the third vertex of a triangle be z

45°+55°+z =180 (linear pair)

z= 180°- 100°

z= 80°

Now, On taking line CD

55°+80°+ PQD= 180°

PQD= 180° - 135°

PQD= 45°

Since , AB and CD are parallel lines

APQ=PQD

y+30°=45°

y=15°

Now , In triangle

x+y+z=180° ( Angle sum property of a triangle)

x+15°+80°=180°

x=180° - 95°

x= 85°

So the values of x and y are 85° and 15° respectively.