Mathematics
In the adjoining figure, ABCD is a cyclic quadrilateral. If ∠BAD = (2x + 5)° and ∠BCD = (x + 10)°, then x is equal to
65
45
55
50
Circles
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Answer
Since, ABCD is a cyclic quadrilateral.
We know that,
The sum of opposite angles of a cyclic quadrilateral is 180°.
⇒ ∠BAD + ∠BCD = 180°
⇒ (2x + 5)° + (x + 10)° = 180°
⇒ 3x° + 15° = 180°
⇒ 3x° = 180° - 15°
⇒ 3x° = 165°
⇒ x° =
⇒ x° = 55°
⇒ x = 55.
Hence, Option 3 is the correct option.
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