# Thread: triangle length vs angles

1. ## triangle length vs angles

What is the value of x in the attached?
all I can think of is EDC = DCA which makes DE also 5 but then I am stuck. The answer should be 10

2. ## Re: triangle length vs angles

Originally Posted by ketanco
What is the value of x in the attached?
all I can think of is EDC = DCA which makes DE also 5 but then I am stuck. The answer should be 10
Yes angle EDC = angle DCA (alternate angles)
Also, angle DCA = angle ECD (because CD bisects angle BCA)

This makes triangle DCE an isosceles triangle and so DE = 5.

Now look at triangle DBE:

angle DBE = angle ACB (since triangle ABC is isosceles)

Also angle ACB = angle DEB (corresponding angles)

So angle DEB = angle DBE, making DBE an isosceles triangle and therefore DB = DE = 5.

Now AC = AB = AD+DB = 6+5 = 11. (I don't agree that the answer is 10, unless EC=4 rather than 5.)

3. ## Re: triangle length vs angles

Originally Posted by Debsta
Yes angle EDC = angle DCA (alternate angles)
Also, angle DCA = angle ECD (because CD bisects angle BCA)

This makes triangle DCE an isosceles triangle and so DE = 5.

Now look at triangle DBE:

angle DBE = angle ACB (since triangle ABC is isosceles)

Also angle ACB = angle DEB (corresponding angles)

So angle DEB = angle DBE, making DBE an isosceles triangle and therefore DB = DE = 5.

Now AC = AB = AD+DB = 6+5 = 11. (I don't agree that the answer is 10, unless EC=4 rather than 5.)
thanks a lot