Measure of the angle between 2 tangent circumferences

Question

$2$ circumferences are external tangent in $Q$, $PA$ and $PB$ are tangents in $A$ and $B$ respectively, and the straight line $t$ is tangent to both circumferences in $Q$. If $\angle APB=80º$, then $\angle AQB=?$

I made a drawing:

Any hints?

Answer 1

Try to explain this: $$\measuredangle AQB=\frac{1}{2}(360^{\circ}-80^{\circ})=140^{\circ}.$$