How to Correct Angle Measurement Errors in Geometry Problems

AI Thread Summary
To correct angle measurement errors in geometry problems, understanding the properties of angles in parallel lines and triangles is essential. For problem 18, the angle m<Q is determined to be 60 degrees by using the concept of vertical angles and the sum of angles in a triangle. In problem 24, the value of x is found to be 40 by applying the properties of isosceles triangles and the relationship between the angles. The discussion emphasizes the importance of recognizing angle relationships and applying geometric principles to solve problems. Mastery of these concepts aids in accurately determining angle measures in various geometric scenarios.
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I'm doing test corrections for homework and we have to explain how to correct what we did wrong. I already have the answers I just need to know how to figure out the answer.

18. Find m<Q. The diagram is not to scale.
http://img100.imageshack.us/img100/3986/helpbp3.jpg

24. Find the value of x. The diagram is not to scale.
Given: <SRT is congruent to <STR, m<SRT=20, m<STU=4x
http://img301.imageshack.us/img301/584/helpep9.jpg
 
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Well, the point is that you need to figure out how to do this. We'll give hints but you need to tells us what you understand about this problem. In the first one, think "Opposite Interior Angles" with parallel lines and "the sum of the angles in a triangle is _____". For the second one, what do you know about isosceles triangles?
 
18. m<Q = 60. Look at the 50 degrees. The angle opposite of that is also 50 degrees, because they are vertical angles. Then, because the two lines are parallel and are cut by a transversal, the alternate interior angles are congruent. So the angle below R is 50 degrees. 70+50 = 120, 180-120 = 60. Since they are vertical angles, then m<Q = 60.24. x = 40. If m&lt;SRT = 20, then m&lt;STR = 20. So 180-20 = 160 = 4x, x = 40
 
HallsofIvy said:
Well, the point is that you need to figure out how to do this. We'll give hints but you need to tells us what you understand about this problem. In the first one, think "Opposite Interior Angles" with parallel lines and "the sum of the angles in a triangle is _____". For the second one, what do you know about isosceles triangles?
Yeah, I did all of the ones I could and I spent about 30 minutes trying to figure these two out and couldn't. Thanks
 
courtrigrad said:
18. m<Q = 60. Look at the 50 degrees. The angle opposite of that is also 50 degrees, because they are vertical angles. Then, because the two lines are parallel and are cut by a transversal, the alternate interior angles are congruent. So the angle below R is 50 degrees. 70+50 = 120, 180-120 = 60. Since they are vertical angles, then m<Q = 60.


24. x = 40. If m&lt;SRT = 20, then m&lt;STR = 20. So 180-20 = 160 = 4x, x = 40
Thanks so much, this helped a lot!
 
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