Advertisements
Advertisements
Question
In the given figure, ABCD is a cyclic quadrilateral. Find the value of x.
Advertisements
Solution
Here, ABCD is a cyclic quadrilateral; we need to find x.
In a cyclic quadrilateral the sum of opposite angles is equal to 180°.
Therefore,
∠ADC + ∠ABC = 180°
⇒ 180° − 80° + 180° − x = 180°
⇒ x = 100°
Hence, the value of x is 100°.
RELATED QUESTIONS
A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.
If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
Prove that a cyclic parallelogram is a rectangle.
Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.
AC and BD are chords of a circle which bisect each other. Prove that (i) AC and BD are diameters; (ii) ABCD is a rectangle.
In any triangle ABC, if the angle bisector of ∠A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.
In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.
In a cyclic quadrilateral ABCD, if ∠A − ∠C = 60°, prove that the smaller of two is 60°
ABCD is a cyclic quadrilateral in BC || AD, ∠ADC = 110° and ∠BAC = 50°. Find ∠DAC.
ABCD is a cyclic trapezium with AD || BC. If ∠B = 70°, determine other three angles of the trapezium.
Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.
ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that AD || BC .
ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that EB = EC.
If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.
The three angles of a quadrilateral are 100°, 60°, 70°. Find the fourth angle.
