How to Correct Angle Measurement Errors in Geometry Problems

[Ebene]

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

 

[HallsofIvy]

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?

 

[courtrigrad]

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 $$m<SRT = 20$$, then $$m<STR = 20$$. So $$180-20 = 160 = 4x$$, $$x = 40$$

 

[Ebene]

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

 

[Ebene]

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 $$m<SRT = 20$$, then $$m<STR = 20$$. So $$180-20 = 160 = 4x$$, $$x = 40$$

Thanks so much, this helped a lot!