In the adjoining figure ABCD is a rhombus. find the measure of the following angles if ACB is equal to 30⁰. If ACB=30⁰. (a) BOC. (b) CBO. (c) OAD. (d) ABO.
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In the adjoining fig. 10.33,ABCD is a rhombus.
Find the measure of the following angles, if ∠ACB=30
∘
(a) ∠BOC
(b) ∠CBO
(c) ∠OAD
(d) ∠ABO
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Solution
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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
.