Finding "x" and the labeled angles.

[arronmercer]

I am having issues with two questions out of my Geometry textbook, the first one being 14. The question is, "Find the value of x. Then find the value of each labeled angle." I do not know how to do this problem nor what it means by labeled angle because the angles are not labeled besides by the equation and "x".


The next question I am having problems with is 23. The question is "Find the values of the variables." I imagine this is pretty simple to do but I cannot grasp it. Any explanations would be greatly appreciated.


Thanks, Arron

 

[pka]

I am having issues with two questions out of my Geometry textbook, the first one being 14. View attachment 2030 The question is, "Find the value of x. Then find the value of each labeled angle." I do not know how to do this problem nor what it means by labeled angle because the angles are not labeled besides by the equation and "x".


The next question I am having problems with is 23. The question is "Find the values of the variables." I imagine this is pretty simple to do but I cannot grasp it. Any explanations would be greatly appreciated.
View attachment 2031

In #14 the two marked angles are supplementary. WHY?

In #23 the angle is a right angle. WHY?

 

[arronmercer]

What?

I don't understand your questions.

 

[pka]

I don't understand your questions.

They are not my questions. They are your questions.
I told how to work them. Then I asked you why that works.
You may not be ready to tackle these. Why don't you talk with your instructor?

 

[Mrspi]

I don't understand your questions.

pka is trying to get you to think about the angles formed when two PARALLEL lines (in your diagrams, the arrows on the lines indicate that the lines are parallel) are cut by a transversal.

You need to look at your textbook to see how angles formed when a transversal cuts two parallel lines are related. You should see that SOME of those angles will always be equal, and SOME of those angles will always be supplementary.

You should also closely examine the sample problems presented in the same section where you'll find those angles discussed. AFTER you've studied the examples, try doing your problems again. If you still need help, please show us what you've done and where you're stuck.

 

[mmm4444bot]

Here is some more information.

This image shows how you visualize the "transversal crossing parallel lines" concept in exercise #14.



For #23, you need to have already memorized the number of degrees in a right-angle. (I'm assuming that you know the meaning of the little square in that diagram.)

Of course, some algebra is required for each of these. You've already taken some algebra, yes?

Cheers ~ Mark :cool:

 

[arronmercer]

Thank you!

Thank you Mark for the visual! I rethought the problem using your photo and the answer it came out to be was correct! And for 23 it makes sense now...I'm in the middle of doing it right now! Thanks again, Arron