Question

Three angles of a quadrilateral are of the measure 130$°$, 82$°$, 40$°$. Find the measure of the fourth angle.

Answer 1

Let the measure of the fourth angle be x°.
Thus, we have:
$$\begin{gathered} 130°+82°+40°+x°=360°[\mathrm{Angle}\mathrm{addition}\mathrm{property}\mathrm{of}\mathrm{quadrilateral}] \\ \Rightarrow 252°+x°=360° \\ \Rightarrow x°=360°-252° \\ \Rightarrow x°=108° \end{gathered}$$
Thus, the measure of the fourth angle of the quadrilateral is 108°.