Question

In the adjoining figure ABCD is a rhombus. Find the values of x and y. Also find the all the angles of the rhombus.

Answer 1

diagonals are perpendicular to each other in a rhombus
so, angle DOA = 90°
now , in triangle DOA,
angle DOA +angle DAO + angle ODA = 180° (angle sum property of a triangle )
90° + 50° + angle ODA = 180°
so , angle ODA = 40°
therefore angle ODA is 'X'
so X is equal to 40°
angle X = angle Y (DA = DB {all the sides of a rhombus ate equal, so the angles opposite to equal sides are equal})
therefore, angle Y = angle X
do, angle Y = 40°
all the angles of rhombus is equal to
angle D = 50° + 40° is 90°
angle A = 50° + 50° is 100°
angle B = 50° +40° is 90°
angle C = 40° +40° is 80°
this is because of angles in the same segments are equal.