ABCD is a rectangle,with angleBAC=42 determine angle DBC - Maths - Quadrilaterals

Question

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

Sunanta Meitei · Accepted Answer

Hi Priyanka!
Here is the answer to your question
<img width="109" height="121" src=
"https://s3mn%20mnimgs%20com/img/shared/userimages/mn_images/image/RECT1%20png"
alt="">
∠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!

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

ABCD is a rectangle,with angleBAC=42.

determine angle DBC.