Question

Help With Geometry.

In a triangle ABC, the interior line BD satisfies that, AD=BC , if the angle A is equal to30°+x, the angle C is equal to 2x° and the angle DBC is equal to 30°-x ,find x.

I,ve Just figure out that the ABD triangle is isosceles . Any idea? Thanks

Answer 1

I wish I could help, but I keep coming up with identities where x drops out. Hopefully someone will see the challenge in this problem. I do see how you got triangle ADB is an isoscelese as angle ADB is also 30 + X degrees making sides AB and DB equal.

Answer 2

ADB is exterior angle, so it is same as sum 30-x+2x = 30+x

Answer 3

but still stuck how to get x :)

Answer 4

Well, i was thinking for draw some auxiliar lines and try to find congruence anywhere, like this

Answer 5

Somehow, I get the feeling there is a relationship between the angle which is 2x and the angle which is 30-x that could be developed......????? other than the sum of (30-x)+2x + angle BDC = 180 degrees. Since there is only information given regarding the angles (no distance measurements), I would assume it can be solved using only the angles, but!! since I can not solve, I am missing something.

Answer 6

@Directrix can you enlighten us here?

Answer 7

No, I cannot. I never got past this statement: I,ve Just figure out that the ABD triangle is isosceles

Answer 8

That statement was based on angles BAD and BDA being equal. I believe that angle ADB is not just 30 degrees as KateNicole posted if it is then x = 0 (not a choice) lol

Answer 9

@KateNicole, please show your reasoning for angle ADB being 30 degrees.

Answer 10

I believe it is (30 + x ) degrees

Answer 11

Nevermind, I didn't see the - x on angle DBC

Answer 12

got it

Answer 13

Here is why I base that: Angle CBD = 180 - 2x -(30 -x) = 150 -x
Now angle ADB would =180-(150-x)= 30 + x in dgrees of course.

Answer 14

x=15

Answer 15

Please show us @bhaskarbabu

Answer 16

i'll do it on paper and upload plz wait

Answer 17

waiting with bated breath.

Answer 18

Good try KateNicole, thanks for trying.

Answer 19

itz way to long to eplain

Answer 20

@Juarismi got it !!!!!!!!

Answer 21

Thanks for clearing that up, but angle ABD sure don't look like a 90 degree right angle lol, but I am convinced now, and being from Missouri, the "show me" state, I am satisfied.