If OD is perpendicular to AB, and ∠DOC = 30°, find ∠BOC - ∠AOC.
![](https://www.edugain.com/egdraw/draw.php?num=3&sx=250&sy=150&A1=cx:100;cy:10;shape:angle;sangle:90;eangle:120;texta:30°;ctextc:D,,C;arcsize:15&A2=cx:100;cy:10;shape:angle;sangle:0;eangle:180.1;noarc:1;textc:B,O,A&A3=shape:polygon;points:100,10,115,10,115,25,100,25 )
Answer:
60°
- According to the question, ∠DOC = 30° and OD is perpendicular to AB.
Therefore, ∠AOD = 90° and ∠BOD = 90°. - Also, ∠DOC + ∠AOC = ∠AOD
⇒ 30° + ∠AOC = 90° (As, ∠AOD = 90° and ∠DOC = 30°)
⇒ ∠AOC = 90° - 30°
⇒ ∠AOC = 60° - Now, ∠BOC - ∠AOC = ∠BOD + ∠DOC - ∠AOC (As, ∠BOC = ∠BOD + ∠DOC)
= 90° + 30° - 60° (As, ∠BOD = 90°, ∠DOC = 30° and ∠AOC = 60°)
= 60° - Therefore, ∠BOC - ∠AOC = 60°