Concept:Angles on a straight line add up to 180∘, and angles around a point add up to 360∘.Explanation:On the straight line PQ, the angles are 80∘, 50∘, x∘, and 10∘.Therefore,80∘+50∘+x∘+10∘=180∘140∘+x∘=180∘x∘=40∘Now consider all the labelled angles around the point.They are 2y∘, 2x∘, 80∘, 50∘, x∘, and 10∘.Their total is 360∘, so:2y∘+2x∘+80∘+50∘+x∘+10∘=360∘Substitute x=40∘:2y∘+80∘+80∘+50∘+40∘+10∘=360∘2y∘+260∘=360∘2y∘=100∘Answer:The angle labelled 2y is 100∘, so the correct option is D.
