Question

In the given figure, find the measure of $\angle ABC$, if $ABCD$ is a cyclic quadrilateral.

• A. ${120}^{\circ }$
• B. ${118}^{\circ }$
• C. ${138}^{\circ }$
• D. ${128}^{\circ }$

Answer 1

The correct option is D ${128}^{\circ }$

Given that: $ABCD$ is a cyclic quadrilateral

$\angle DCB=82°$

$\angle DCA=46°$

$\angle CYB=62°$

$\angle ACB=\angle DCB-\angle DCA=82-46=36°$

Consider $△CYB$

$\angle CBY=180°-\angle BCY-\angle CYB=180°-62°-36°=82°$ (sum of three angles of a triangle is 180°)

Also, $\angle ACD=\angle ABD=46°$ ......... (angles in the same segment)

Thus, $\angle ABC=\angle ABD+\angle CBY=(82+46)°=128°$

Answer: $\angle ABC=128°$