# Prove two angles are equal

• July 15th 2009, 07:42 AM
BG5965
Prove two angles are equal
Hi, here is the question:

http://i301.photobucket.com/albums/n.../Problem12.png

I'm not exactly sure how this is solved, but I'm thinking similar triangles/congruency is involved as some smaller triangles share sides, perpendicular angles etc.

$\widehat{MAQ}=90-\widehat{AMQ}$
$\widehat{PAK}=90-\widehat{APK}$
But PMQA is a cyclic quadrilater and $\widehat{AMQ}=\widehat{APK}$
Therefore, $\widehat{MAQ}=\widehat{PAK}$