Answer:
[tex]\widehat{DE}=70^{\circ}[/tex]
Step-by-step explanation:
We have been given a circle. We are asked to find measure of minor arc DE.
We know that the circumference of circle is equal to 360 degrees. We can set an equation using our given information.
[tex]\widehat{AB}+\widehat{BC}+\widehat{CD}+\widehat{DE}+\widehat{EF}+\widehat{FA}=360^{\circ}[/tex]
[tex]20^{\circ}+30^{\circ}+40^{\circ}+\widehat{DE}+110^{\circ}+90^{\circ}=360^{\circ}[/tex]
[tex]\widehat{DE}+290^{\circ}=360^{\circ}[/tex]
[tex]\widehat{DE}+290^{\circ}-290^{\circ}=360^{\circ}-290^{\circ}[/tex]
[tex]\widehat{DE}=70^{\circ}[/tex]
Therefore, measure of minor arc DE is 70 degrees.
