Textbook question

Question

The question is: Given QE is the perpendicular bisector of ZN, QN= 5x-5, ZE= 2x+1, and ZQ= 3x+3, determine ZN.

Answer 1

Q

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Z E N

^ Sounds like from your comments that the triangle looks like this.

A perpendicular bisector cuts a line into 2 equal parts. Therefore, ZE and EN must be equal to each other.

ZE is 2x+1 so we need to know what x is to get the answer.

How can we solve for x?

Well, if QE is perpendicular to ZN, then QN must be equal to QZ

Therefore we can say that 3x+3 = 5x-5 and solve for x. (I'll leave that for you to do)

The question asks you to find the value of ZN, (which is ZE + EN) Since we know that ZE and EN are the same value, once you find the value of ZE you should be able to get the answer.

Let me know if you have any questions!

Answer 2

ZQ must equal QN because if a point is on a perpidicular bisector of a segment, then it is equidistant from the endpoints of the segment.

So 3x + 3 = 5x - 5 and x = 4. ZE thus equals 2(4) + 1 = 9 and because QE bisects ZN, ZN must be equal to twice that (18).