In the given figure, O is the centre of the circle and AB is the diameter of the circle. If difference of ∠COD and ∠DBC is 25°, then find the measure of ∠DEB.
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Given : O is the centre of the circle and AB is the diameter of the circle. difference of ∠COD and ∠DBC is 25°
To Find : the measure of ∠DEB.
Solution:
∠COD = 2∠DBC angle be same arc CD at center and remaining circle
∠COD = ∠DBC + 25°
=> 2∠DBC = ∠DBC + 25°
=> ∠DBC = 25°
∠ADB = 90° as AB is diameter
∠CDB = 180° - ∠ADB ( linear pair)
=> ∠CDB =90°
∠DBC + ∠CDB + ∠DEB. = 180° ( sum of angles of triangle)
=> 25° + 90° + ∠DEB. = 180°
=> ∠DEB. = 65°
measure of ∠DEB. = 65°
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