In the adjoining figure ABCD is a rhombus if <OAB=30°,find the measure of <OD and<ABC.​

From the figure:-

∠DAO=∠BCO (Alternate interior Angle)

=30

o

(Two parallel lines are crossed by a transversal)

We know that Diagonals in a rhombus intersect at right angle so ∠BOC=90 …………..(1)

through vertically opposite Angles AOD=90

o

Now takes ΔBOC

∠BOC+∠OCB+∠CBO=180

o

90

o

+30

o

+∠CBO=180

o

∠CBO=180−120

o

∠CBO=60

o

……………(2) Ans

∠OCB=∠OAD (Alternate interior Angle)

=30

o

…………..(3) Ans

All the four triangle should be similar by this in ΔAOB.

∠AOB=90

o

∠OAB=30

o

∠ABO=60

o

.

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