Question

Which of the following pair of angles are opposite angles of a cyclic quadrilateral?

• A. ${130}^{\circ }$, ${40}^{\circ }$
• B. ${123}^{\circ }$, ${57}^{\circ }$
• C. ${60}^{\circ }$, ${80}^{\circ }$
• D. ${90}^{\circ }$, ${80}^{\circ }$

Answer 1

The correct option is B ${123}^{\circ }$, ${57}^{\circ }$

Sum of the opposite angles of a cyclic quadrilateral is ${180}^{\circ }$

Then option A

$\Rightarrow {130}^{\circ }+{40}^{\circ }={170}^{\circ }$

Hence the sum is not equal to ${180}^{\circ }$

Option B

$\Rightarrow {123}^{\circ }+{57}^{\circ }={180}^{\circ }$

The sum is equal to ${180}^{\circ }$