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Class 9
>>Maths
>>Circles
>>Cyclic Quadrilaterals
>>In the given figure, BD = DC and CBD =
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In the given figure, BD=DC and ∠CBD=30
o
, find ∠BAC.
1715703
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Medium
Updated on : 2022-09-05
Solution
verified
Verified by Toppr
It is given that BD=DC
From the figure we know that
∠BCD=∠CBD=30
Consider ∠BCD
Using the angle sum property
∠BCD+∠CBD+∠CDB=180
By substituting the values
30
+30
+∠CDB=180
On further calculation
∠CDB=180
−30
By subtraction
So we get
∠CDB=120
We know that the opposite angles of a cyclic angles of a cyclic quadrilateral are supplementary
It can be written as
∠CDB+∠BAC=180
120
+∠BAC=180
∠BAC=180
−120
∠BAC=60
Therefore, ∠BAC=60
Answer: angle ADC = 60°
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Answers & Comments
Step-by-step explanation:
search-icon-header
Search for questions & chapters
search-icon-image
Class 9
>>Maths
>>Circles
>>Cyclic Quadrilaterals
>>In the given figure, BD = DC and CBD =
Question
Bookmark
In the given figure, BD=DC and ∠CBD=30
o
, find ∠BAC.
1715703
expand
Medium
Updated on : 2022-09-05
Solution
verified
Verified by Toppr
It is given that BD=DC
From the figure we know that
∠BCD=∠CBD=30
o
Consider ∠BCD
Using the angle sum property
∠BCD+∠CBD+∠CDB=180
o
By substituting the values
30
o
+30
o
+∠CDB=180
o
On further calculation
∠CDB=180
o
−30
o
−30
o
By subtraction
∠CDB=180
o
−30
o
−30
o
So we get
∠CDB=120
o
We know that the opposite angles of a cyclic angles of a cyclic quadrilateral are supplementary
It can be written as
∠CDB+∠BAC=180
o
By substituting the values
120
o
+∠BAC=180
o
On further calculation
∠BAC=180
o
−120
o
By subtraction
∠BAC=60
o
Therefore, ∠BAC=60
o
Answer: angle ADC = 60°
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