Question
Sat October 27, 2012 By: Amithjose

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

Expert Reply
Sat October 27, 2012
 
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
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