Question

The points $A,B,C,D,E$ are marked on the circumference of a circle in clockwise direction such that $\angle ABC={130}^{\circ }$ and $\angle CDE={110}^{\circ }$. The measure of $\angle ACE$ in degrees is

• A. ${50}^{\circ }$
• B. ${60}^{\circ }$
• C. ${70}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

We know that, sum of opposite angles in a cyclic quadrilateral is ${180}^{\circ }$.
Consider cyclic quadrilateral $ABCE$,
$\angle ABC={130}^{\circ }\therefore \angle AEC={180}^{\circ }-{130}^{\circ }={50}^{\circ }$
Consider cyclic quadrilateral $ACDE$,
$\angle CDE={110}^{\circ }\therefore \angle CAE={180}^{\circ }-{110}^{\circ }={70}^{\circ }$
In $\Delta ACE$,
$\angle ACE={180}^{\circ }-{70}^{\circ }-{50}^{\circ }={60}^{\circ }$