Answer
$x= 140^{\circ}$
Work Step by Step
Let the smaller angles be denoted by A and B
since Sum of Angles of a Triangle = 180
Then in bigger triangle 2$\angle$A + 2 $\angle$B +100 =180
2($\angle$A +$\angle$B )=$80
THUS
\angle$A +$\angle$B = 40
In Smaller triangle $\angle$A + $\angle$B +$\angle$X = 180
40 +$\angle$X = 180
$\angle$X = $140^{\circ}$
