Question

If one angle of cyclic quadrilateral is ${{70}^{\circ }}$, then the angle opposite to it is:
A). ${{20}^{\circ }}$
B). ${{110}^{\circ }}$
C). ${{140}^{\circ }}$
D). ${{160}^{\circ }}$

Answer 1

Hint: As mentioned in the question a cyclic quadrilateral is a cycle polygon which has a circumscribed circle. The sum of opposite angles of a cyclic quadrilateral is ${{180}^{\circ }}$

Complete step by step solution: As in the corner on cycle quadrilateral the sum of opposite angles of a cyclic quadrilateral are supplementary, $A-c$ the sum is equal to ${{180}^{\circ }}$
Now, is the question we have been given one of the angles as ${{70}^{\circ }},$ let the angle which needs to be found is $x$.
Then, according to the theorem above we can sevy,
               $x+{{70}^{\circ }}={{180}^{\circ }}$
Solving the above equation,
               $x=180-70$
               $x={{110}^{\circ }}$
$\therefore $ option B) ${{110}^{\circ }}$ is the right answer.

Note: In a cyclic quadrilateral, the sum of the angles around the centre of the circle is ${{360}^{\circ }}$ degrees. The sum of the angles in each of the triangles is ${{180}^{\circ ''}}$degrees using this property, it has been proved that opposite angles in a cyclic quadrilateral are supplementary.