Need geometry help

[Hot Lava Mama]

Can someone help us figure out how to get to the answer?

 

 

Here's the best I can do for a picture:

 

                                      B

 

 

                                      D

 

 

                  A                                C

 

 

 

Imagine there are lines as follows: AB to BC to AC to make a triangle.  Then, AD to DC to AC to make a smaller triangle within the bigger one sharing the same bottom line of AC.

 

 

 

Given: line AB congruent to line BC, angle DAC congruent to angle BCD, measure of angle B is 50.  Find measure of angle ADC.

 

Here is what we figured out: since AB = BC, the triangle is an isosceles, so angles BAC = BCA.  Therefore, angle BAD also = to DCA.  But we can't go any further. 

The answer is 115, but we can't figure out how they got there.

 

Anyone a geometry wizard?

:)

Hot Lava Mama

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[MicheleinMN]

Because AB = BC the corner angles for each line to are equal.  Angle CAB = ACB with angle B= 50 (given) means that each angle is 65 (180 - 50=130 and that divided by 2 equals 65).  We also know that the corner angles are bisected by AD and CD meaning they are 1/2 of the original angles, so they equal 32.5 each or 65 total.  180 - 65 = 115.

 

Does that help?

[EKS]

You could also do it this way:

 

You know that angle BAC and angle BCA are each 65 degrees.  Say that angle DAC (and angle BCD)=x.  That means that angle DCA=65-x.  Therefore angle ADC=180-(x+65-x) which is 115.

[Hot Lava Mama]

Thanks!  That's it!

:)