ABCD is a rectangle,with angleBAC=42.
determine angle DBC.
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)
∠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.