Answer: The measure of non-reflex ∠DOB is 108° and the measure of reflex ∠DOB is 252°.
Explanation:
It is given that the reflex angle ∠DOB has measure of 3.5y while the measure of ∠AOD is y.
From the given figure we can say that angle AOC and COB are supplementary angles and their sum is 180 because they are lies on a straight line.
[tex]\angle DOB=\angle AOD+\angle AOC+\angle COB[/tex]
[tex]3.5y=y+180[/tex]
[tex]3.5y-y=180[/tex]
[tex]2.5y=180[/tex]
[tex]y=72[/tex]
Therefore the value of y is 72.
[tex]\angle DOB=3.5y[/tex]
[tex]\angle DOB=3.5\times 72[/tex]
[tex]\angle DOB=252[/tex]
Therefore the reflex and is 252 degree.
The measure of non-reflex ∠DOB is,
[tex]\angle DOB=360-252=108^{\circ}[/tex]
Therefore, the measure of non-reflex ∠DOB is 108° and the measure of reflex ∠DOB is 252°.
