ABCD Is quadrilateral inscribed in a circle such that BC =9cm ,BA=7.2cm,CBA=51 and ACD=29 calculate angle DC
To find angle DC, we will use the property of an inscribed angle which states that the measure of an inscribed angle is half the measure of its intercepted arc.
Since angle CBA is given as 51 degrees, we know that arc CA is twice that angle or 102 degrees. Similarly, arc BA is twice angle ACD or 58 degrees.
The sum of the angles of a quadrilateral is 360 degrees. Therefore, angle DC is 360 degrees minus the sum of angles ACD and CBA.
ACD = 29 degrees
CBA = 51 degrees
Angle DC = 360 degrees - (29 degrees + 51 degrees) = 280 degrees