Question

Point M is in the exterior of an angle AOB, ray OC is a bisector of this angle. Prove, that the measure of angle MOC is equal to one-half the sum of the measures of angles AOM and BOM.

Answer 1

see the prove below

Explanation:

We have to prove that MOC=(AOM+BOM)/2

Let Angle AOM=x and AOC=y . => AOB=2y ( because OC is the bisector of AOB)

So MOC= AOM+AOC=x+y

BOM=AOB+AOM=2y +x

AOM+BOM= x+2y+x=2y+2x

(AOM+BOM)/2= (2y+2x)/2=x+y=MOC

The statement is proved