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Question

# In the given figure, ABCD is a kite with AC and BD as diagonals and ∠ABC = 30∘. Find x.

A

75

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B

80

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C

85

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D

70

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Solution

## The correct option is A 75∘ From the figure, the diagonal AC divides the kite into two isoceles triangles. In △ABC, AB=CB (Adjacent sides of kite ABCD ) Given, ∠ABC = 30°. Since, AB=BC,∠BAC=∠BCA Then, ∠BCA=∠BAC=x By, angle sum property of a triangle, ∠ABC+∠BCA+∠BAC = 180° ⇒30°+x+x=180° ⇒30°+2x=180° ⇒2x=180°−30°=150° ⇒x=75° Hence, the value of x is 75°.

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