Question

One of the base angle a cyclic trapezium is double the other. What is the measure of the larger angle?

• A. ${60}^0$
• B. ${80}^0$
• C. ${75}^0$
• D. ${120}^0$

Answer 1

Answer: (D)

${120}^0$

In cyclic trapezium,

Sum of opposite angle $={180}^o$ ...[opposite angles of a cyclic quadrilateral are supplementary].

Let the smaller angle be $x$

and larger angle $=2x$.

Then, $2x+x={180}^o⟹3x={180}^o⟹x={60}^o$.

Therefore, Larger angle $=2x=2\times {60}^o={120}^o$.

Hence, option $D$ is correct.