ABCD is a kite If Angle BCD=40 degree, find(i) Angle BDC (ii) Angle ABC Please answeritby tomorrow - Maths - Understanding shapes

Question

ABCD is a kite If Angle BCD=40 degree, find(i) Angle BDC (ii) Angle
ABC Please answeritby tomorrow

Neha Sethi · Accepted Answer

Dear student

Given: ABCD is a kite and ∠BCD=40°We know that in a kite smaller diagonal bisects the angle
⇒∠BCA=∠ACD=12∠BCD=40°2=20°and also diagonals  of kite bisect each other at 90°so, ∠AOD=∠AOB=∠BOC=∠COD=90°In △DOC, by angle sum property of △⇒∠DOC+∠OCD+∠CDO=180°⇒90°+20°+∠CDO=180°⇒∠CDO=180°-110°⇒∠CDO=70°=∠BDCNow AB=BC⇒∠BCA=∠BAC=20°    angles oppoite equal sides are equal
Now in △ABC , by angle sum property of △⇒∠ABC+∠BCA+∠CAB=180°⇒∠ABC+20°+20°=180°⇒∠ABC=180°-40°⇒∠ABC=140°
Regards

ABCD is a kite. If Angle BCD=40 degree, find(i) Angle BDC (ii) Angle ABC . Please answeritby tomorrow