Answer:
119°
Step-by-step explanation:
First we must determine the angle of E, we can do so by getting the sum of the intersecting arcs and then dividing by 2 as such:
[tex]\frac{1}{2}(82+40)=61[/tex]
This means m∠AED and m∠BEC are both 61°. Since we're trying to figure out what m∠DEC is we have to understand that AC and BD are both straight lines and as such are 180°. Therefore, since we know one of the angles that make up that straight line, the answer will be the difference of those angles as such:
180°-61°=119°
And so m∠DEC=119°
