# Geometrical problem

## Homework Statement

Suppose ABC is a triangle, where ∠ABC = ∠ACB =80°. A line BD through B meets AC at D such that
∠DBC=60°.Similarly CE meets AB at E where ∠ECB = 50°. Whats the value of ∠EDB?

## The Attempt at a Solution

I solved the problem using coordinate geometry but i was asked to solve it using simple geometry.

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tiny-tim
Homework Helper
hi projjal!
… i was asked to solve it using simple geometry.
show us your diagram, with all angles marked, and all equal distances marked

sorry for that. i have uploaded the diagram.

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Let's denote the intersection of EC and BD by F. Can you find the angles at this point F?

Can you find the angle at A?

tiny-tim
Homework Helper
mark all the angles, and all equal distances

(and preferably re-draw it so that those 80° angles look like 80°)

preferably re-draw it so that those 80° angles look like 80°
I think now it should be okay with the diagrams.I have also marked all the angles.
now whats EDB ???

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tiny-tim
Homework Helper
ah , that's much better!
also BE = BC

hmm … i can't see any obvious way to find EDB

(longshot: i wonder whether it has anything to do with 40° being twice 20° ?)

Draw a line in D parallel to BC.

pbuk
Gold Member
If you extend DE and CB until they meet at a point P, can you find angle EPB?

If you extend DE and CB until they meet at a point P, can you find angle EPB? .

Draw a line in D parallel to BC.
I couldnot get anything from that.If you could do it please specify it to me.

pbuk
Gold Member
EPDF form a quadrilateral, the other 3 angles are known.

EPDF form a quadrilateral, the other 3 angles are known.
If P is the point of intersection of DE & CB how EPDF forms a quadrilateral?

pbuk
Gold Member
If P is the point of intersection of DE & CB how EPDF forms a quadrilateral?
Sorry, EPBF - not enough screen area to see the diagram and type at the same time!

haruspex
Homework Helper
Gold Member
Sorry, EPBF - not enough screen area to see the diagram and type at the same time!
We know PBF and BFE. What's the third?
I don't think it's going to be that simple anyway. Seems to me these angles have been chosen quite carefully. It's no coincidence that there are isosceles triangles all over the place which would not be so if we were to change just one of the given angles.

So thats how its done.

pbuk