In the given figure determine the value of y and hence find (EOB,(FOA and (COD - Maths - Lines and Angles

Question

In the given figure determine the value of y and hence find
(EOB,(FOA and (COD

Neha Sethi · Accepted Answer

From the figure ∠EOF=∠COD  Vertically opposite angles⇒∠EOF=∠COD=5y  
*Now ∠BOC+∠COD+∠DOA=180°   Linear pair⇒5y+5y+2y=180°⇒12y=180°⇒y=15°  
1Now ∠FOE+∠EOB+∠BOC=180°  Linear pair⇒5y+∠EOB+5y=180°  ⇒∠EOB+10y=180°⇒∠EOB+1015° =180°    using 1⇒∠EOB+150°=180°⇒∠EOB=30°Now, ∠EOF+∠FOA+∠AOD=180°    Linear pair⇒5y+∠FOA+2y=180°⇒∠FOA+7y=180°⇒∠FOA+715°=180°    using 1⇒∠FOA=180°-105°=75°So, ∠FOA=75°and ∠EOF=∠COD=5y   using *⇒∠COD=5y    ⇒∠COD=5×15°=75°   using 1⇒∠COD=75°