Question

In the given figure O is the centre of the circle angle ADC is equal to 110 degree and chord BC is equal to chord BE find the measure of angle CBE

Answer 1

The measure of ∠CBE is 140°

∠ADC = 110°  ( Given )

BC = CE. ( Given )

∠BCE = ∠ BEC ( Opposite angles to equal sides are equal ).--- 1

In Δ BME and Δ BCE

BC = BE ( As BC = CE)

∠ BCE = ∠ BEC ( From 1 )

BM = MB ( common side )

Therefore, by SAS congruence Δ BME ≅ Δ BCE

∠CBM = ∠ EBM ( By CPCT ) --- 2

Since, ABCD is a cyclic quadrilateral, thus -

∠D + ∠CBM = 180°

∠CBM = 70°

∠CBM + ∠CBE = 70°+70° ( from 2 )

∠CBE = 140 °

Answer 2

Answer:  

Step-by-step explanation: