Question

Quadrilateral ABCD is inscribed in OZ such that
and mZBZC = 78. Find mZDCA.

Answer 1

39°

Explanation:

Since, angle formed on the circumference of the circle is half of the angle formed at the centre of the circle.

`\therefore m\angle BAC = (1)/(2) * m\angle BZC\\\\</p><p>\therefore m\angle BAC = (1)/(2) * 78°\\\\</p><p>\therefore m\angle BAC = 39°\\\\</p><p>\because In\: \square ABCD, \: AB ||DC... (Given) \\\\</p><p>\therefore \angle DCA \cong \angle BAC.. (Alternate\: \angle 's) \\\\</p><p>\therefore m\angle DCA=m \angle BAC\\\\</p><p>\huge \purple {\boxed {\therefore m\angle DCA=39°}}`