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Lines and Angles — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsLines and Angles4 Marks
Question
In the given figure, two straight line AB and CD intersect at a point O. If $\angle\text{AOC} = 42^\circ,$ find the measure of each of the angles:
  1. $\angle\text{AOD}$
  2. $\angle\text{BOD}$
  3. $\angle\text{COB}$
✓

Answer


AB and CD intersect at O and CD is a straight line.
  1. $\angle\text{COA}+ \angle\text{AOD}= 180^\circ$ (linear pair)
$42^\circ+ \angle\text{AOD} = 180^\circ$

$\angle\text{AOD} = 138^\circ$
  1. $\angle\text{COA}$ and $\angle\text{BOD}$ are vertically opposite angles.
$\therefore\angle\text{COA} = \angle\text{BOD} = 42^\circ$ [from (i)]
  1. $\angle\text{COB}$ and $\angle\text{AOD}$ are vertically opposite angles.
$\therefore\angle\text{COB} = \angle\text{AOD} = 138^\circ$ [from (i)]

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