A city planning engineer in Cleveland must check the 10 angles that make up the three intersections on the map of downtown. If any of the angles formed by the intersections of the streets is greater than 135°, different road signs have to be used due to a new rule created by city council. She knows CED = 52 degrees and that FJG = 64 degrees, so she knows she will NOT need a protractor to measure the unknown angles.
Q7: Which angle is vertical to CED?
A: AEC
B: AEB
C: BED (my answer)
D: AED
Q8: What is the measure of the angle in your #7 answer? (short answer, my answer was 52 degrees)
Q9: Which angle is vertical to FJG?
A: FJH
B: GJI
C: HJI (my answer)
D: FJI
Q10: What is the measure of the angle in your #9 answer? (short answer, my answer was 64 degrees)
I don't have a problem with geometry, I really don't. For some reason, the new Common Core testing system doesn't line up with the lessons I am currently learning online. I would like the answers, but more than anything, just explain to me how to find the vertical angles and use them to find the measure of the angle!
Also for some reason I can't post a picture, I'll try and find a way to do it
Do not trust the Steve guy I almost failed cause of him
To find the vertical angle, you need to understand that vertical angles are formed by the intersection of two lines. Vertical angles are opposite to each other and have equal measures. Here's how you can find the answers and measures for each question:
Q7: Which angle is vertical to CED?
To find the angle that is vertical to CED, you need to identify the angle that intersects with CED and is opposite to it. Looking at the options, we see that angles AEC and BED intersect with CED, but only BED is opposite to CED. Therefore, the correct answer is C: BED.
Q8: What is the measure of the angle in question #7?
Since vertical angles have equal measures, the measure of angle CED is the same as the measure of the vertical angle BED. Given that CED has a measure of 52 degrees, the measure of angle BED is also 52 degrees.
Q9: Which angle is vertical to FJG?
To find the angle that is vertical to FJG, you need to identify the angle that intersects with FJG and is opposite to it. Looking at the options, we see that angles FJH and HJI intersect with FJG, but only HJI is opposite to FJG. Therefore, the correct answer is C: HJI.
Q10: What is the measure of the angle in question #9?
Again, since vertical angles have equal measures, the measure of angle FJG is the same as the measure of the vertical angle HJI. Given that FJG has a measure of 64 degrees, the measure of angle HJI is also 64 degrees.
I hope this explanation helps you understand how to identify vertical angles and find their measures. If you have any further questions or need clarification, feel free to ask!
For Q7, I disagree. Vertical angles share only the intersection. I don't have the diagram, but I can't see how CED and BED can be vertical angles, since D is on both of them.
Q9 looks like a better possibility.