$SS_{1}=6cm$
$SS_{2}=8cm$
$S_{1}S_{2}=10cm$
Gọi $SS_{1}∩G_{1}=H_{1}$; $SS_{2}∩G_{2}=H_{2}$; $G_{1}∩G_{2}=O$
Ta có: $SS_{1}²+SS_{2}²=6²+8²=100$
$S_{1}S_{2}²=10²=100$
$⇒SS_{1}²+SS_{2}²=S_{1}S_{2}²$
$⇒ΔSS_{1}S_{2}$ vuông tại $S$
Xét tứ giác $SH_{1}OH_{2}$ có:
$\widehat{H_{1}SH_{2}}+\widehat{SH_{2}O}+x+\widehat{OH_{1}S}=360^{0}$
$⇔90^{0}+90^{0}+x+90^{0}=360^{0}$
$⇒x=90^{0}$