Question

two lines AB and CD intersect at 'o'. Find angle AOC ,angle COB ,angle BOD & angle DOA. If angleAOC+angleCOB+angleBOD=270°

Answer 1

Can you give diagram???

Answer 2

Step-by-step explanation:

<AOC = <BOD = 90°

<AOD = <COB = 90°

Step-by-step explanation:

Given:

AB and CD intersect at O.

<AOC + <COB + <BOD = 270°

Proof:

<AOC = <BOD = x ( Vertically opposite angles )

<AOD = <COB = y

<AOC + <COB + <BOD + <DOA = 360°

=> x + y + x + y = 360°

/* Sum of the angles around a point */

=> 270 + y = 360

=> y = 360 - 270

=> y = 90°

Now ,

<AOC + <COB = 180° ( Linear pair )

=> x + y = 180°

=> x = 180° - y

=> x = 180° - 90° = 90°

Therefore,

<AOC = <BOD = x = 90°

<AOD = <COB = y = 90°

Hope this helps u