Parallelogram angle finding problem?

Question

All right, this one has me a little stumped.

There's a parallelogram ABCD. Let point E be the intersection of the diagonals.

Angle AED is 60 degrees.
Angle BAE is 40 degrees.

Is it possible to find Angle CBD, and if so, can someone tell me how?

Thanks!

P.S. This is not homework, just a problem I found on the net, but there's no answer provided :(

Answer 1

It can be found. Ill provide a PARTIAL solution that proves uniqueness and tell you how to finish it. Its easier on pen and paper to actually calculate.

Proof:

Angle AED = 60 So that Angle AEB = 120 degrees since the sum of the two is a straight line and must add to 180.

So angle EBA is 20 degrees since triangle AEB must add to 180.

Now we know that AE = EC = b and that DE = EB = a.

So that for a given a; b is fixed and that EBC is a class of triangles congruent to the triangle with an angle 60 degrees and sides 1, b/a adjecent to that angle.

Thus angle CBD = angle CBE which is determined uniquely.

i say uniquely since by given a we have b, and thus b/a but one dimension only determines size of a parallelagram. Thus if we set a = 1 then it is a basis for the congruence class of parallellograms with the given angles.

So we know there is a solution. How to find it?

1 ) Find b given a = 1.

Triangle ABE has angles {40,20,120} and sides {1, b, c}

So by sin law

sin 20 / b = sin 40 / a

b = sin 20 / sin 40

Thus also by the sin law

sin CBE / b = sin 60 / c

We can find c from the cos law

c ^ 2 = 1 + b ^ 2 - 2 b cos 60

and thus we can find CBE. Do the math

Answer 2

No, it is not possible.

In a parallelogram as the one described the angles satisfy
A = C, B = D and A+B = 180

With the information provided if AED = 60 degrees that means that CED is 120, DCE = BAE = 40 degrees and CDE = 20 degrees.

You are looking for CBD (let's call it x) which is equal to ADE
You can also define EAD = CBE (let's call it y) and all you know is that x + y = 120

Therefore there is a whole family of paralelograms that satisfy your initial condition (i.e. x (or CBD) can be 60 if y is 60 or x can be 40 if y is 80). The family being defined by x + y = 120

Answer 3

well, i dont really get the point of having point E? but uhm... just look on the parallelogram and find the angle thats diagonally across from from angle cbd, and that's going to have the same angle measurement as cbd. so if aed is diagonally across from cbd, the the angle measurement of cbd is 60 degrees. but thats ONLY if its a regular paralellogram. meaning opposite side lengths are equal and two pairs of equal angles.

but i dont think thats going to be the case here, bcuz 60+40 is 100 and if the other two angles are 60 and 40, they'd all b acute angles and the total degrees will b 200, nt 360 degrees. so thats probably nt a regular paralellogram.

so i dont think u can figure it out without using a protractor... sry

Answer 4

There are 2 39 deg angles and a pair of 141 degree angles. The sum of the angles in 2 consecutive vertices of any paralellogram is a hundred and eighty tiers If a is the smaller attitude, then a + (3a+ 24) = a hundred and eighty sparkling up for a i'm getting a = 39 and the different attitude is 141 tiers. examine those effects.

Answer 5

The angles you can find are:
m(angle ACD) = 40° [AIA with angle BAC]
m(angle BEC) = 60° [Vert to angle AED]
m(angle AEB) = m(angle CED) = 120° [Supp to angle AED]

Other than that, you're out of luck without more information.
m(angle CBD) + m(angle ACD) = 120°, but that's as close as you can get to finding m(angle CBD) without more info.

Sorry.

Answer 6

if you had i pic i have better idea but u can do to the fact a parallelogram are two lines pass though two parallel lines that from two travel so now you have < . at that from 180 dreegs so line ac and BC are 180 dreegs so yes you can find

Answer 7

angle cbd is=120 degrees. i cant explain it here but trust me its correct.i can only tell one thing:angle dec=120 degrees

Answer 8

in a parallellogram any angle is equal to the angle directly across from it