Question

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

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

Answer 1

The correct option is B ${60}^o$

$\angle ABC=130°$

and $\angle CDE=110°$

Joining $AC$ and $CE$

In quadrilateral $ABCE$

$\angle ABC+\angle AEC=180°=130°+\angle AEC=180°=\angle AEC=50°$

In quadilateral $AEDC$

$\angle CDE+\angle CAE=180°110°+\angle CAE=180°\angle CAE=70°$
In $△ACE$

$\angle CAE+\angle AEC+\angle ACE=180°\angle ACE=60°$