ABCD is a rectangle,with angleBAC=42.

determine angle DBC.

Hi Priyanka!

Here is the answer to your question.

∠BAC = 42°.

Let the diagonals AC and BD intersect in O

∴ OB = OC (Diagonals of rectangle are equal and bisect each other)

In DOBC, OB = OC

⇒ ∠OCB = ∠OBC (Equal sides have equal angles opposite to them)

In DABC,

∠BAC + ∠ABC + ∠ACB = 180° (angle sum property)

⇒ 42° + 90° + ∠ACB = 180°

⇒ ∠ACB = 180° – 132° = 48°

∴ ∠OBC = 48° (∠OCB = ∠OBC)

Thus, the measure of ∠DBC is 48°

Hope! You got the answer.

Cheers!

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