9. The diagram shows a kite ABCD. The diagonals cut at right angles and
intersect at O. What is the length of the diagonal AC?
Answers
hshshsbsbb babababahahah
Step-by-step explanation:
MATHS
□ABCD is a kite in which diagonal AC and diagonal BD intersect at point O. ∠OBC=20
o
and ∠OCD=40
o
Find ∠ABC
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ANSWER
□ABCD is a kite where AC and BD are diagonals intersect at point O.
∠OBC=20
o
and ∠OCD=40
o
.
We know, in kite diagonals intersect at right angles.
∴ ∠AOD=∠DOC=∠BOC=∠AOB=90
o
In △BOC,
⇒ ∠BOC+∠OBC+∠OCB=180
o
⇒ 90
o
+20
o
+∠OCB=180
o
⇒ 110
o
+∠OCB=180
o
∴ ∠OCB=70
o
⇒ AB=BC [ Adjacent sides are equal in length ]
⇒ ∠ACB=∠BAC=70
o
[ Angles opposite to equal sides are equal ]
In △AOB,
⇒ ∠ABO+∠AOB+∠OAB=180
o
⇒ ∠ABO+90
o
+70
o
=180
o
⇒ ∠ABO=20
o
⇒ ∠ABC=∠ABO+∠OBC
=20
o
+20
o
=40
o
∴ ∠ABC=40
o
.
solution