Question

In the given kite, y equals

(a) 37°

(b) 28°

(c) 20°

(b) 40°

Answer 1

Correct option is (b) 28°

Given, ABCD is a kite,

Let the diagonals are meeting at O.

In △ABD and △BCD

AB = BC (Given)

AD = CD (Given)

BD = BD (Common)

Thus, △ABD ≅ △CBD (SSS rule)

Thus, ∠DBA = ∠CBA  (by CPCT)  .....(1)

Now, In △OAB and △OCB

∠OBA = ∠OBC (From 1)

OB = OB (Common)

AB = BC (Given)

△OAB ≅ △OCB (SAS rule)

Thus, ∠AOB = ∠COB = \(\frac{180°}2\) = 90°   (Equal angles by CPCT)

Now, In △OAB

∠OAB + ∠OBA + ∠OAB = 180°

37° + 2y − 3° + 90° = 180°

2y = 56°

y = 28^∘