Question

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Answer 1

Answer:

In the given figure:

The reflex angle $\angle DOB=3y$ and $\angle AOD = y$

$\angle COB = \angle AOD = y$  [By vertical angle theorem]

From the given we can say that:

$\angle AOC$ and $\angle COB$ are supplementary angles.

Supplementary angles states that the two measure are add up to 180 degree.

⇒ $\angle AOC +\angle COB = 180^{\circ}$          .....[1]

then; the reflex angle DOB is:

$\angle DOB = \angle AOD + \angle AOC + \angle COB$

Substitute the given values we get;

$3.5y=y+180^{\circ}$

Subtract y from both sides we get;

$2.5 y = 180^{\circ}$

Divide both sides by 2.5 we get;

$y = 72^{\circ}$

$\angle DOB = 3y = 3.5(72) =252^{\circ}$

We have to find the non reflex $\angle DOB$

Non reflex angle DOB is;

$\angle DOB = 360^{\circ}-252^{\circ} = 108^{\circ}$

Therefore, the non-reflex angle DOB is 108 degree.