ABC is a kite in which angle OBC =20 and angle OCD = 35 find : 1 Angle ABC - Maths - Understanding Quadrilaterals

Question

ABC is a kite in which angle OBC =20 and angle OCD = 35 find : 1
Angle ABC , angle ADC and angle BAD

Lovina Kansal · Accepted Answer

Dear student

We know, in kite diagonals intersect at right angles
So, ∠AOD=∠DOC=∠BOC=∠AOB=90°In △BOC, by angle sum property of triangle∠BOC+∠OBC+∠OCB=180°90°+20°+∠OCB=180°∠OCB=70°Also, AB=BC   adjacent sides are equal in length
⇒∠ACB=∠BAC=70°     [Angles opposite to eqaul sides are equal]In △AOB, By angle sum property of triangle∠ABO=180°-∠AOB-∠OAB=180°-90°-70°=20°Also, AD=DC   adjacent sides are equal in length
⇒∠DAC=∠DCA=35°     Angles opposite to equal sides are equalIn △COD,By angle sum property of triangle ∠COD+∠DCO+∠CDO=180°90°+35°+∠CDO=180°∠CDO=55°Similarly,∠ADO=55°So, ∠ADC=∠CDO+∠ADO=55°+55°=110°So, ∠BAD=∠DAO+∠BAO=35°+70°=105°and ∠ABC=∠ABO+∠OBC=20°+20°=40°

ABC is a kite in which angle OBC =20 and angle OCD = 35 find : 1. Angle ABC , angle ADC and angle BAD