Answer:
In the given figure:
The reflex angle [tex]\angle DOB=3y[/tex] and [tex]\angle AOD = y[/tex]
[tex]\angle COB = \angle AOD = y[/tex] [By vertical angle theorem]
From the given we can say that:
[tex]\angle AOC[/tex] and [tex]\angle COB[/tex] are supplementary angles.
Supplementary angles states that the two measure are add up to 180 degree.
⇒ [tex]\angle AOC +\angle COB = 180^{\circ}[/tex] .....[1]
then; the reflex angle DOB is:
[tex]\angle DOB = \angle AOD + \angle AOC + \angle COB[/tex]
Substitute the given values we get;
[tex]3.5y=y+180^{\circ}[/tex]
Subtract y from both sides we get;
[tex]2.5 y = 180^{\circ}[/tex]
Divide both sides by 2.5 we get;
[tex]y = 72^{\circ}[/tex]
[tex]\angle DOB = 3y = 3.5(72) =252^{\circ}[/tex]
We have to find the non reflex [tex]\angle DOB[/tex]
Non reflex angle DOB is;
[tex]\angle DOB = 360^{\circ}-252^{\circ} = 108^{\circ}[/tex]
Therefore, the non-reflex angle DOB is 108 degree.
