Advertisements
Advertisements
Question
ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
In a cyclic quadrilateral, the sum of opposite angles is 180°.
Now, ∠A + ∠C = 90° + 95° = 185° ≠ 180°
And ∠B + ∠D = 70° + 105° = 175° ≠ 180°
Here, we see that, the sum of opposite angles is not equal to 180°.
So, it is not a cyclic quadrilateral.
APPEARS IN
RELATED QUESTIONS
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.
If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
In the figure m(arc LN) = 110°,
m(arc PQ) = 50° then complete the following activity to find ∠LMN.
∠ LMN = `1/2` [m(arc LN) - _______]
∴ ∠ LMN = `1/2` [_________ - 50°]
∴ ∠ LMN = `1/2` × _________
∴ ∠ LMN = __________
In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.
ABCD is a cyclic quadrilateral in ∠DBC = 80° and ∠BAC = 40°. Find ∠BCD.
ABCD is a cyclic quadrilateral in ∠BCD = 100° and ∠ABD = 70° find ∠ADB.
Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.
ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that EB = EC.
ABCD is a cyclic quadrilateral such that ∠ADB = 30° and ∠DCA = 80°, then ∠DAB =
In a cyclic quadrilaterals ABCD, ∠A = 4x, ∠C = 2x the value of x is
