In figure, ∠ACD=120∘ and ∠APB=100∘ ,
(i) find x and y.
(ii) If ∠BAC=2.5y, find ∠ABC.
(i)x+100∘=180∘ [Linear pair of angles]
⇒x=80∘
Now, we have,
x+y=120∘ [Sum of interior opposite angles is equal to the exterior angle]
⇒80∘+y=120∘
⇒y=40∘
So, x=80∘,y=40∘.
(ii)∠BAC=2.5y,
∠BAC=2.5×40∘=100∘
∠BAC+∠ABC=120∘ [Sum of interior opposite angles is equal to the exterior angle]
⇒∠ABC=120∘−100∘
⇒∠ABC=20∘