Question 94

In a Rhombus ABCD, measure of angle CAB is 30°, what is the measure of angle ABC?

Solution

Given : ABCD is a rhombus and $$\angle$$ CAB = 30°

To find : $$\angle$$ ABC = ?

Solution : Diagonals of a rhombus bisect each other at 90° and also bisect the angles of the rhombus.

In $$\triangle$$ AOB

=> $$\angle$$ AOB + $$\angle$$ OBA + $$\angle$$ BAO = 180°

=> 90° + 30° + $$\angle$$ OBA = 180°

=> $$\angle$$ OBA = 180° - 120° = 60°

$$\therefore$$ $$\angle$$ ABC = $$2 \times$$ $$\angle$$ OBA

= $$2 \times 60 = 120$$°

=> Ans - (B)


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