Question

Find the measure of $\angle CED$

• A. ${70}^{\circ }$
• B. ${80}^{\circ }$
• C. ${120}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is A ${70}^{\circ }$

from the figure

AOC is a straight line

$\angle AOB+\angle BOC=180⟹\angle BOC=180-80=100$

$\angle CEB=\frac{1}{2}\angle BC={50}^{\circ }$

In triangle BCO

$OB=OC⟹\angle OCB=\angle OBC$( Angle opposite to equal side are equal)

$\angle OBC+\angle OCB=180-100=80⟹\angle OCB=\angle OBC={40}^{\circ }$

As DCBE is cyclic quadrilateral

$\angle EDC+\angle CBE=180⟹\angle EDC=180-120=60$

AS BE||CD

$\angle DEB+60=180⟹\angle DEC+50=180-60⟹\angle DEC=120-50={70}^{\circ }$