Question

Consider the diagram below. What is the measure of arc DEB?

PLEASE HELP!!!


A. 76

B.146

C. 177

D.183

Answer 1

146

Explanation:

Answer 2

Option B.
`146\°`

Explanation:

we know that

The inscribed angle is half that of the arc it comprises.

`m<DEB=(1)/(2)(arc \ BCD)`

substitute the values

`107\°=(1)/(2)(arc \ BCD)`

`arc \ BCD=214\°`

Remember that

`arc \ DEB+arc \ BCD=360\°` -----> complete circle

substitute the value of arc BCD and solve for arc DEB

`arc \ DEB+214\°=360\°`

`arc \ DEB=360\°-214\°=146\°`