Question

Two straight line AB and CD intersect one another at the point O. If angle AOC + angle COB +angle BOD =274 degrees, then angle AOD=​

Answer 1

$\large\underline{Diagram:-}$

$\large\underline{Questions:-}$

• Two straight line AB and CD intersect one another at the point O. If angle AOC + angle COB +angle BOD =274 degrees, then angle AOD.

$\large\underline{Given:-}$

• Two straight line AB and CD intersect one another at the point O.
• If angle AOC + angle COB +angle BOD =274 degrees,

$\large\underline{To find:-}$

• find the Angle AOD ...?

$\large\underline{Solutions:-}$

Let us draw the diagram showing two line AB and CD intersect at a point O.

$\: \: \: \: \: Thus,$

$\: \: \: \: \: \: \: \angle AOD, \: \angle AOC, \: \angle COD and \angle BOD$

$\: \: \: \: \: \therefore \: \: Form \: \: a \: \: complete \: \: angle, \: \: that \: \: is \: \: sum \: \: of \: \: the \: \: angle \: \: is \: \: {360} \degree$

$\: \: \: \: \: \: \: \angle AOD \: + \: \angle AOC \: + \: \angle COD \: + \: \angle BOD \: \: = \: \: {360} \degree \: \: \: \: \: ....{(i)}.$

$\: \: \: \: \: And$

$\: \: \: \: \: Given \: \: that$

$\: \: \: \: \: \: \: \angle AOC \: + \: \angle COD \: + \: \angle BOD \: \: = \: \: {274} \degree \: \: \: \: \: ....{(ii)}.$

$\: \: \: \: \: \therefore \: \: Subtracting \: \: Eq. \: \: {(i)} \: from \: Eq. \: \: {(ii)} \: \: we \: \: get.$

$\: \: \: \: \: \angle AOD \: \: = \: \: {360} \degree \: - \: {274} \degree$

$\: \: \: \: \: \angle AOD \: \: = \: \: {86} \degree$

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Answer 2

${ \bold{ \text{Given:-}}}}$

• ${ \bf \angle \: aoc + \angle \: cob + \angle \: bod = 274}$

${ \bold{ \text{To \: Find:-}}}$

• ${ \bf \angle \: aod}$

${ \bold{ \text { Solution:-}}}$

${ \bf \angle \: aod + \angle \: aoc + \angle \: cob + \angle \: bod = 360}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ({ \sf \because \: complete \: angle})$

$\implies{ \bf \angle \: aod + 274 = 360}$

$\implies{ \bf \angle \:aod = 360 - 274}$

${ \boxed{ \sf{ \pink {\angle \: aod = 55}}}}$

So angle AOD = 55

Angle Names :-

• Acute Angle

• Right Angle

• Obtuse Angle

• Straight Angle

• Reflex Angle

• Zero Angle

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