Question

Help with a geometry problem, triangles.

In a triangle ABC, it draws the interior line BD, for which AD=BC , if the angle A is 54°, the angle C is 24° y the angle DBC is x, find x.

We are supposed to find some congruent triangles here.

Any idea.?

Answer 1

Lets draw the triangle first.

Answer 2

does it give you a figure already?

Answer 3

Here is the graph.

Answer 4

okay give me a minute to open up the file :)

Answer 5

The answer is E. 18degrees

Answer 6

Let me draw you a graph

Answer 7

this is just a way to look at the question and of course youhave many ways of solving this question.

Answer 8

so you know that the line where the 54, y, x and 24 degrees become a 180 degree supplementary line. so we do 180-54-24=120, so we know that x+y=102

Answer 9

then you look again and see oh x and y are not complementary angels. that means they must be smaller than 90 degrees. a biggest not angel not equal to 90 degrees is 89. so 102-89=13, lets start from the closest #, 102-10=92, wrong, its bigger than 90 degrees, 102-15=93, still wrong, 102-18=84! Bingo, thats the one.

Answer 10

on the last post I meant 180-54-24=102

Answer 11

thats the elimanate watyy to do it.

Answer 12

Does that make sense?

Answer 13

Well, it´s clear for me that x+y=102, but where does come from that they both must be less than 90?

Answer 14

because using the triangel identities that if BDU is a obese angle then that means there cannot be any other angle bigger than 90 degrees. and if n a nother trianglethere are two angles together added up more than 90 degrees the third angle is not a90 degree angle.

Answer 15

@jokereq7 The problem don´t say anithing about obtuse triangles, all the information given is the measures of those angles and that AD = BC.

And if this is this reasoning is correct, why they say that AD=BC?
Shouldn´t that information be used in order to solve the problem?

By this reasoning the answer could be any angle above 12°, why not 15°?
What do you think?

Answer 16

Answer is 10

Answer 17

@bhaskarbabu Can you show us how did you get that result?

Answer 18

in the same way as we did the day before yesterday

Answer 19

But here the triangle ABD is not isosceles. Its altitude is not median.

How we could relate the sides AD and BC drawing an altitude?

Answer 20

first draw an altitude and find how it divides AD then continue as the previous one

Answer 21

if AD= a then assume the parts of AD as 'a' and 'a-y'
then find y

Answer 22

So i get a sin(24) = (a-y)tan(54)
And tan (24+x) = [asin(24)]/y

Well, solve y in terms of a may take a while without a calculator.

Doing with a calculator i get that the a factor cancels and i get.

tan( 24 + x) = 0.58

And x=10 don´t satisfies that.
Where i (or the calculator) went wrong ?