Find the Angle

THUDandBLUNDER

Posers and Puzzles

02 May 05

THUDandBLUNDER

Joined: 29 Feb 04
Moves: 22

02 May 05

1 edit

The isosceles triangle ABC has AB = AC and angle BAC = 20 degrees.

The point D lies on AC such that angle DBC = 60 degrees.
The point E lies on AB such that angle ECB = 50 degrees.

Find angle CED.

Bowmann

Non-Subscriber

RHP IQ

Joined: 17 Mar 05
Moves: 1345

02 May 05

1 edit

Do you mean an isosceles triangle?

0 degrees?

THUDandBLUNDER

Joined: 29 Feb 04
Moves: 22

02 May 05

Originally posted by Bowmann
Do you mean an isosceles triangle?

0 degrees?

Yeah, thanks for the correction.
Have amended the wording.

davegage

Joined: 04 Aug 01
Moves: 2408

02 May 05

Originally posted by THUDandBLUNDER
The isosceles triangle ABC has AB = AC and angle BAC = 20 degrees.

The point D lies on AC such that angle DBC = 60 degrees.
The point E lies on AB such that angle ECB = 50 degrees.

Find angle CED.

I get that angle CED must be 80:

Without going through every step, I solved the following set of equations simultaneously. The equations follow from the Law of Sines and from the problem statement:

AD/[sin(130 - CED)] = AE/[sin(30 + CED)];
AE/sin(30) = AC/sin(130);
AD/sin(20) = AB/sin(140);
AB = AC;

Solving this set of equations, I get CED = 80.

THUDandBLUNDER