I do not know, if ray bisects an angle? Does it means it cuts it in "1/2"?

Question

Ray PL lies in the interior of an angle RPH, m angle RPL = x-5 and m angle LPH = 2x+18. If m angle HPR = 58, find the measure of the smallest angle formed.                      Let: 2x+18 =58    2x=40   and x=20    The answer m angle RPL =10.   From what I had learn insofar, if an anlge is bisect by a ray, line. or segment the angle is cut in 1/2; thus, my answer divide by 1/2 would be 10? But what I learn is when an angle bisector cut an angle the angle would be congruent. The problem above does not give that. Would you help? How did it come to be 10.  I solve the equation: x-5+2x+18 =58     3 x=58-13     x=15   and substiute in x-5 the smallest angle is 10. I just made some error in adding the coefficient with the variable.

Comments

In your question the ray PL splits the angle into two unequal angles, so it doesn’t bisect RPH in this case.

If you’re told that a ray does bisect an angle, or the ray is the bisector, then it’s true that the angle is split into two equal halves, because “bisect” means “cut in half”.

Answer 1

Ray PL lies inside angle RPH(or HPR) .It does not mean it bisects the angle .

m angle RPL + m angle LPH=m angle RPH

x-5+2x+18=58

3x+13=58

3x=58-13=45

x=45/3=15

m angle RPL=x-5=15-5=10