Question

ABCD is a rhombus such that ∠ACB = 40°. Then find the measure of∠ADB.
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Answer 1

Answer:

Diagonals of a rhombus are perpendicular bisectors of each other and thus BOC is 90°.

In triangle boc, obc+ocb+cbo=180

obc=180-(40+90)

obc=180-130= 50°

Now, in triangles BOC and DOA,

boc=doa (vertically opp)

oa=oc (diagonals bisect each other)

bo=do (diagonals bisect each other)

Thus, triangle BOC is congruent to DOA by SAS congruency rule.

Thus, angle cbo=ado=50°

ADO is the same as ADB. Thus, answer is 50°