In the figure ABCD is a square. A line segment DX cuts the side BC at X and the diagonal AC at O such that COD = 105o and OXC = y. Then y is equal to

 

Answer : Given :In the figure ABCD is a square. A line segment DX cuts the side BC at X and the diagonal AC at O such that COD = 105 degree and OXC = y

To find :y 

 

Since DX is a line segment, then 

angle COD + angle COX = 180 degrees {Angle sum property}

=> angle COX = 180 -105 = 75 degrees........(1)

 

Since ABCD is a square and AC is a diagonal , therefore all the angles in a square is 90 degree each and AC bisects the angle in half. {property}

=> angle ACB {  also OCX } = 90 /2 =45 degrees...............(2)

 

 

In traingle COX 

=> angle OCX + angle COX  + y = 180 degree { sum of angles in a triangle is 180 degree}

=> y = 180 - (45+75) {using eq 1 and 2}

=> y = 60 degrees Answer