Question

23. In Figure 13, lines AB, CD and EF intersect at 0. Find the measures of ZAOC and ZCOF.​

Answer 1

/_AOE and /_EOB are linear pair of angles.

/_AOE+/_EOB = 180°

/_AOE+/_DOE+/_BOD=180°

⇒ /_DOE=180°-40°-35° = 105°

Vertically opposite side angles are equal

/_DOE=/_COF=105°

Now, /_AOE+/_AOF=180° [ Linear pair] ⇒

/_AOE+/_AOC+/_COF=180°

⇒ 40°+/_AOC +105° = 180°

⇒ /_AOC = 180°-145°

⇒/_AOC=35°

[ Vertically opposite angle are equal]

Hence,/_AOC=35° and /_COF=105°