Answer:
Step-by-step explanation:
We are given that, ABCD is RHOMBUS, whose diagonals meet at O.
As We know The diagonals of the rhombus intersect each other perpendicularly, so :
[tex] \sf \angle AOB = \angle BOC = \angle COD = \angle DOA = 90\degree [/tex]
Now,
In [tex] \sf\Delta AOB [/tex], using angle sum property which states that the sum of the interior angles of any triangle is always equal to [tex] \sf 180\degree [/tex].
[tex] \sf \angle A + \angle O + \angle B = 180\degree [/tex]
[tex] \sf 35\degree + 90 \degree + x = 180\degree[/tex]
[tex] \sf 125 + x = 180\degree [/tex]
[tex] \sf x = 180\degree - 125\degree[/tex]
[tex] {\boxed{ \sf{ x = 55\degree}}} [/tex]
In [tex] \sf\Delta AOD [/tex],
[tex] \sf\angle OAD = \angle OAB = 35\degree [/tex] ( In a rhombus, the diagonals bisect each other and also bisect the opposite angles)
Using angle sum property,
[tex] \sf \angle A + \angle O + \angle D = 180\degree [/tex]
[tex] \sf 35\degree + 90\degree + y = 180\degree [/tex]
[tex] \sf 125 + y = 180\degree[/tex]
[tex] \sf y = 180\degree - 125\degree[/tex]
[tex] {\boxed{ \sf{y = 55\degree}}} [/tex]
