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

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) (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) (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

RELATED QUESTIONS
A triangle ABC, where |AB| = |AC|, a line CD is drawn from angle C and intersects side AB (answered by CPhill,greenestamps,ikleyn,math_tutor2020)
Triangle ABC is isosceles with AB = AC. Let D be the foot of the altitude from A on BC,... (answered by math_helper)
In triangle ABC, side AB is x longer than side BC . The ray bisecting angle B intersects... (answered by robertb)
ABC is a triangle with base = BC . A line segment DE is drawn parallel to Side AC. D is... (answered by ikleyn)
ABC is a right angle isosceles triangle, angle BCA = 90, with BC as the base and AB as... (answered by ikleyn)
Suppose that M lies on the side BC of triangle ABC, and angle BAM = angle CAM = a. Let... (answered by mananth,greenestamps)
(1)Find the value of an isosceles triangle with its side ABC such that line AB is... (answered by Aldorozos)
In triangle ABC, linr CD is both the median and the altitude to side AB. If AB=5x+3,... (answered by ankor@dixie-net.com)
Given an isosceles triangle ABC, where C is the vertex angle and the legs AC = BC = 10,... (answered by ikleyn,josgarithmetic)