SOLUTION: ABC is an isosceles triangle with side AB= side AC. Line BC is produced to D such that side AC=side CD. If angle ABC = 2x°, angle BAC=x° and angle ADC=y°, prove that x=y

Algebra ->  Triangles -> SOLUTION: ABC is an isosceles triangle with side AB= side AC. Line BC is produced to D such that side AC=side CD. If angle ABC = 2x°, angle BAC=x° and angle ADC=y°, prove that x=y      Log On


   

Question 1169821: ABC is an isosceles triangle with side AB= side AC. Line BC is produced to D such that side AC=side CD. If angle ABC = 2x°, angle BAC=x° and angle ADC=y°, prove that x=y
Found 2 solutions by mananth, math_tutor2020:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
AB=AC
B=C=2x
In triangle ABC x+2x+2x =180
5x =180
x = 36 deg
In triangle ACD 2y+3x=180
plug x=36
2y+108=q80
2y =72
y=36 deg
x=y
.


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Refer to the drawing that tutor mananth made.
However, keep in mind that points B, C, and D should be on the same straight line.

AC = CD leads to angles CAD and ADC being congruent. They are denoted as y in the drawing.
This similar line of logic also explains why angleABC = angleBCA = 2x.

From here we can use the remote interior angle theorem
angleCAD + angleADC = angleBCA
y+y = 2x
2y = 2x
y = x
x = y