Question

Two lines AB and CD intersect at o.if /AOC+/COB+/BOD=270°,find the measures of /AOC,/COB,/BOD and/DOA

Answer 1

Answer:

<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°

•••♪

Answer 2

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