Circle with centre C, and points A,B,D and E on the circumference of the circle. BD is the diameter of the circle. Angle CDA is 18 deg and angle AED is 31 deg. Find angle EDA.
Circle theorem: angle in a semi-circle is a right angle.Therefore angle BAE = 90 + 31 = 121 degrees ABDE is a cyclic quadrilateral and:Circle theorem: Opposite angles in a cyclic quadrilateral sum to 180 degrees.BAE is opposite CDE.CDE = 180 -121 = 59 degrees Therefore EDA = 59-18 = 41 degrees.
