Question

Two lines AB and CD intersect each other at a point O such that `angleAOC : angleAOD=5 : 7`. Find all the angles.

Answer 1

Correct Answer - `angleAOC=75^(@)=angleBOD, angleAOD=105^(@)=angleBOC`
Let `AOC=(5x)^(@)` and `angleAOD=(7x)^(@)`.
`angleAOC+angleAOD=180^(@) implies 5x+7x=180 implies 12x=180 implies x=15`.
`:. angleAOC=(5xx15)^(@)=75^(@) and angleAOD=(7xx15)^(@)=105^(@)`.
`angleBOD=angleAOC=75^(@)` [vertically opposite `angles`]
`angleBOC=angleAOD=105^(@)` [vertically opposite `angles`].