Mathematics
In the given figure, O is the centre of a circle and ABE is a straight line. If ∠CBE = 55°, find :
(i) ∠ADC
(ii) ∠ABC
(iii) the value of x.
Answer
(i) We know that,
In a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
∠ADC = ∠CBE = 55°
Hence, ∠ADC = 55°.
(ii) From figure,
∠CBE + ∠ABC = 180° [Linear pairs]
∠ABC = 180° - 55°
∠ABC = 125°.
Hence, ∠ABC = 125°.
(iii) We know that,
Angle which an arc subtends at the centre is double that which it subtends at any point on the remaining part of the circumference.
∠AOC = 2∠ADC
∠AOC = 2(55°)
∠AOC = 110°
The reflex angle AOC,
x° = 360° - angle AOC
x° = 360° - 110°
x° = 250°.
Hence, x = 250.
Related Questions
In the given figure, ABCD is a cyclic quadrilateral whose side CD has been produced to E. If BA = BC and ∠BAC = 40°, find ∠ADE.
In the given figure, AB is a diameter of a circle with centre O and chord ED is parallel to AB and ∠EAB = 65°. Calculate : (i) ∠EBA (ii) ∠BED (iii) ∠BCD
In the given figure AB and CD are two parallel chords of a circle. If BDE and ACE are straight lines, intersecting at E, prove that Δ AEB is isosceles.
In the given figure, the two circles intersect at P and Q. If ∠A = 80° and ∠D = 84°, calculate :
(i) ∠QBC
(ii) ∠BCP
