Given the trapezoid as shown and unknown angles
Note that the sum of angles in a quadrilateral is 360⁰
Hence,
[tex]\begin{gathered} (2x+20)+2x+(2x-10)+(3x-10)=360^0 \\ 2x+2x_{}+2x+3x+20-10-10=360^0 \\ 9x=360^0 \\ x=\frac{360}{9}=40^0 \end{gathered}[/tex]
The missing angles can then be calculated to be:
[tex]\begin{gathered} m\angle L=(2x+20)=2(40)+20=100^0 \\ m\angle M=(3x-10)^0=3(40)-10=110^0 \\ m\angle N=(2x-10)^0=2(40)-10=90^0 \\ m\angle P=2x=2(40)=80^0 \end{gathered}[/tex]
