We know that the sum of measures of internal angles in each quadrangle is 360°.
Look at the picture.
[tex] \alpha+\beta+\gamma+\delta=360^o\ \text{and}\ \delta+\tau=360^o\\\\\text{therefore}\\\\\alpha+\beta+\gamma+\delta=\delta+\tau\ \ \ |-\delta\\\\\alpha+\beta+\gamma=\tau [/tex]
Therefore we have:
[tex]\theta=35^o+83^o+23^o=141^o[/tex]
Answer: θ = 141 deg.
