See complete Problem 184 at:

www.gogeometry.com/problem/p184_triangle_angles_problem.htm

Triangle and angles. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Friday, September 26, 2008

### Elearn Geometry Problem 184

Labels:
angle,
angle bisector,
isosceles,
Problem 184,
triangle

Subscribe to:
Post Comments (Atom)

x=32

ReplyDeleteEvrenin, the answer x = 32 is not correct, try again. Good luck.

ReplyDeletex=30. I have an algebraic proof. Antonio, do you have a geometric one?

ReplyDeleteOrange Skid

Yes, I have a geometric solution.

ReplyDeleteThank you for your question.

Angle ABD=58 which makes angle ABC = 88 and angle ACB =44. AC/AD=sin(x+16)/sin(x) =AC/AB=sin(88)/sin(44) which leads us to a simple equation like: sin(x+16)/sin(x) = 2cos(44) which gives x=30 deg since sin(46)=cos(44). Thus, x=30 deg.

ReplyDeleteI still would like to know how this done by plane geometry alone.

Ajit: ajitathle@gmail.com

Problem 184

ReplyDeleteForming an equilateral triangle ADE (E is above the AC),then AB=AE=AD=ED .But <EAB=4,

<EBA=(180-4)/2=88=58+30, so<EBD=30. Then B, E,C are collinear.But <EDB=2,<DEC=32, so

<EAC=44=<ECA ,so EC=AE.Therefore E is the center of the circle triangle ADC so

<ACD=<AED/2=60/2=30.

APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE