Question

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ },\angle ACD$ is ${50}^{\circ },$ find $\angle ADC$.

• A. ${60}^{\circ }$
• B. ${80}^{\circ }$
• C. ${50}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is A

${60}^{\circ }$

$\angle DBC={70}^{\circ }\text{and}\angle ACD={50}^{\circ }$

$\angle DBC=\angle DAC$
[Angles produced on the circle by the same segment will be equal]

$\angle DAC={70}^{\circ }$

$\text{In}\Delta ADC,$

$\angle DAC+\angle DCA+\angle ADC={180}^{\circ }$
[Sum of angles in triangle]

${70}^{\circ }+{50}^{\circ }+\angle ADC={180}^{\circ }$

$\angle ADC={180}^{\circ }-{120}^{\circ }$

$\angle ADC={60}^{\circ }$