Question

One angle of a cyclic trapezium is double the other. What is the measure of the larger angle?
(a) $60{}^\circ $
(b) $80{}^\circ $
(c) $75{}^\circ $
(d) $120{}^\circ $

Answer 1

Hint: For solving this problem, first we consider the opposite angle property of cyclic trapezium. by using this property and the given information in the problem statement we proceed for obtaining our answer.

Complete step-by-step answer:
In geometry, a cyclic quadrilateral is a quadrilateral having all the vertices lying on a circle. The circle is known as a circumscribed circle and all the vertices are said to be concyclic.

Therefore, a cyclic trapezium has all the vertices lying on a circle. Since the trapezium has a pair of parallel lines, so the opposite angle sum is supplementary.
Let one of the angles be x. The other angle will be 2x. By using the above property, the sum of both the angles is 180 degrees.
$\begin{align}
  & x+2x=180{}^\circ \\
 & 3x=180{}^\circ \\
 & x=\dfrac{180{}^\circ }{3} \\
 & x=60{}^\circ \\
\end{align}$
Therefore, the larger angle is $2x,\text{ that is }120{}^\circ $.
Hence, option (d) is correct.

Note: The key concept involved in solving this problem is the knowledge of cyclic quadrilateral specifically cyclic trapezium. Student must be aware of the supplementary angle property to solve the problem without error.