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horrorfan [7]
4 years ago
8

I will award brainliest!!

Mathematics
1 answer:
mart [117]4 years ago
7 0

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.


     

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