Question

In the figure below, angle with arc1 and angle with arc2 are adjacent angles:

Line AB is shown. Point C lies between points A and B and a ray extends from point C. Angle 1 is created by the ray and segment AC while angle 2 is created by the ray and segment CB.

Write an indirect proof proving that the sum of angle with arc1 and angle with arc2 is 180°.

Answer 1

@Mertsj

Answer 2

Assume that the m<1 + m<2 is not 180
Show that the assumption leads to a contradiction.

Answer 3

ok..

Answer 4

@Mertsj what goes after the assumption ?

Answer 5

Show that m<1+m<2 does equal 180

Answer 6

m<1 + m<2 equals a straight line

Answer 7

straight lines = 180

Answer 8

@Mertsj

Answer 9

Yes.

Answer 10

Yes. That is right.

Answer 11

@Mertsj

Answer 12

@Notamathgenius

Answer 13

Can you see that I have replied to you?

Answer 14

What do you think is next?

Answer 15

well i would say this: Assume that the sum of m<1 + m<2 is not 180°. It is given that m<1 and m<2 are adjacent angles. m<1 and m<2 both equal 90°. 90 + 90 = 180 so the sum of m<1 and m<2 is 180°.

Answer 16

@Mertsj idk if im correct tho

Answer 17

Well but you don't know that both angles are 90 degrees. You do know that their non-adjacent sides are opposite rays.

Answer 18

And therefore the sum of the two angles is 180. Therefore the assumption is false and m<1+m<2=180

Answer 19

so i take out the 90 degrees statements and put: sum of the two angles is 180 which makes the assumption false ?

Answer 20

@Mertsj

Answer 21

or can i put that they create a straight line and straight lines equal 180

Answer 22

yes

Answer 23

@ganeshie8

Answer 24

@Australopithecus @whpalmer4 @thomaster @Isaiah.Feynman these guys are really smart...may be able to help you.

Answer 25

thanks

Answer 26

Prove that the sum of two adjacent angles whose non-adjacent sides are opposite rays is 180.
Given: Point C between A and B on segment AB. <1 with side AC and ray extending from point C. <2 side BC and ray extending from point C.
Prove: m<1+m<2=180
1. Assume that m<1+m<2 is not equal to 180
2. CA and CB are opposite rays 2. Given
3. <1 and <2 are adjacent angles 3. Given
4. <1 and < 2 are supplementary 4. Adjacent angles whose non-common
sides are opposite rays are supplementary
5. m<1+m<2 = 180 5. Definition of supplementary angles
6. The assumption that m<1+m<2 is not 180 is false and the sum of two adjacent angles whose non-adjacent sides are opposite rays is 180.