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Question
ABCD is a cyclic quadrilateral in BC || AD, ∠ADC = 110° and ∠BAC = 50°. Find ∠DAC.
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Solution
It is given that BC || AD , `angleADC = 110°` and `angleBAC = 50°`
We have to find `angleDAC`
In cyclic quadrilateral ABCD
`angleA + angleC = 180°` ..… (1)
`angleB + angleD = 180°` ..… (2)
Since, `angleADC = 110°`
So,
`angleB = 180° - angleD`
`=180° - 110°`
= 70°
Therefore in Δ ABC , 50° + 70° + ` angle BCA `= 180°
So , `angleBCA` = 60° ..… (3)
Now, `angleBCA = angle CAD ` (BC || AD and AC is transversal)
`⇒ angle BCA = angle CAD` = 60°
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