Question

Find the possible pairs of the opposite angles for a inscribed quadrilateral.

• A. ${110}^o,{70}^o$
• B. ${65}^o,{25}^o$
• C. ${11}^o,{169}^o$
• D. ${123}^o,{69}^o$

Answer 1

Answer: (A), (C)

${11}^o,{169}^o$

A cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose all vertices lie on a single circle.

The sum of opposite angles of a quadrilateral inscribed in a circle is ${180}^o.$

For example, $\angle D+\angle B={180}^o.$

Option (b): ${65}^o+{25}^o={90}^o$
Hence, this is not correct.

Option (c): ${11}^o+{169}^o={180}^o$
Hence, this is correct.

Option (d): ${123}^o+{69}^o={192}^o$
Hence, this is not correct.