Triangle ABC is isosceles with AB=BC. There is a point D on AC such that BD = DC and AB=AD.
What is the measure of angle BAC?
Angle ABD=angle ADB=α.
Angle BAD=angle DBC=angle DCB=β.
Angle BDC=180-2β.
Angle ADB+Angle BDC=180, so α+180-2β=180, so
α=2β.Angle ABC=α+β.
Draw a parallel to AC through B.
The two new angles with vertex B are both β, so
α+β+2β=180.
Combining both equalities shown in bold, 5β=180, so β=36.
Edited on September 1, 2004, 10:04 am
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Posted by Oskar
on 2004-09-01 09:57:08 |
Simple
