Question

Find the value of x and each missing angle.M(2x + 20° (3x – 10)2xP(2x – 10)Nx=m ZL=mZM=mZN=m ZP=Blank 1: :Blank 2:Blank 3:Blank 4:Blank 5:

Answer 1

Given the trapezoid as shown and unknown angles

Note that the sum of angles in a quadrilateral is 360⁰

Hence,

`\begin{gathered} (2x+20)+2x+(2x-10)+(3x-10)=360^0 \\ 2x+2x_{}+2x+3x+20-10-10=360^0 \\ 9x=360^0 \\ x=(360)/(9)=40^0 \end{gathered}`

The missing angles can then be calculated to be:

`\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}`