Question

in the given figure ab is a diameter of a circle with centre o and CD is parallel to BA. ​

Answer 1

METHOD 1. USING PARALLEL LINES AND TRANVERSAL PROPERTIES
given that,
AB||CD,
<DCA = 20°
Now AC is transversal
so <DCA = <CAO
Or, <CAO = 20°
Also AO = CO
Therefore ∆AOC is an isosceles ∆.
so, <CAO = <ACO [angle opposite to equal sides of ∆]
<ACO = 20°
METHOD 2. USING DIAGONAL PROPERTY OF QUADRILATERALS
Since the diagonals bisect angles at vertex so,
<ACO = <DCA
<ACO = 20°