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Lines And Angles — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsLines And Angles3 Marks
Question
Two lines AB and CD intersect at O. If $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=270^\circ,$ find the measure of $\angle\text{AOC},\angle\text{COB},\angle\text{BOD}$ and $\angle\text{DOA}.$
✓

Answer

Given:$\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=270^\circ$
To find:$\angle\text{AOC},\angle\text{COB},\angle\text{BOD},\angle\text{DOA}$
Here,$\angle\text{AOC},\angle\text{COB},\angle\text{BOD}=270^\circ$[Complete angle]
⇒ 270 + AOD = 360 ⇒ AOD = 360 - 270 ⇒ AOD = 90 Now, AOD + BOD = 180 [Linear pair] 90 + BOD = 180 ⇒ BOD = 180 - 90 ⇒ BOD = 90 AOD = BOC = 90 [Vertically opposite angles] BOD = AOC = 90 [Vertically opposite angles]

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