# Angles Problem

• Jun 30th 2012, 08:45 AM
Telo
Angles Problem
Attachment 24193

Here are two mirrors OD and OE the angle between them is "alpha"

The question is to find angle "beta"

• Jun 30th 2012, 09:58 AM
richard1234
Re: Angles Problem
Angle-chasing usually works:

$\angle OBA = 90-\alpha$

$\angle DBC = 90-\alpha$ (due to symmetry)

$\angle ABC = 2 \alpha$ (since OBA + DBC + ABC = 180 deg)

$\angle ACB = 90 - 2\alpha$

$\angle EC(D) = 90 - 2\alpha$ (also due to symmetry)

$\angle BC(D) = \beta = 4 \alpha$ (since ACB + EC(D) + BC(D) = 180 deg)
• Jun 30th 2012, 10:46 AM
Telo
Re: Angles Problem
thanks very much but why are <OBA and <DBC equal? they are not similar triangles please explain ;(
• Jun 30th 2012, 11:02 AM
richard1234
Re: Angles Problem
It's because the ray reflects at point B, so the angle of incidence equals the angle of reflection.