Respuesta :
We have been given an image of a trapezoid. We are asked to find the measure of angle M and N.
We know that bases of trapezoid are parallel and the two angles between two parallel lines are supplementary, so we can set an equation as:
[tex]\angle M+\angle N=180[/tex]
[tex](6y-10)+(4y-10)=180[/tex]
[tex]6y-10+4y-10=180[/tex]
[tex]10y-20=180[/tex]
[tex]10y-20+20=180+20[/tex]
[tex]10y=200[/tex]
[tex]\frac{10y}{10}=\frac{200}{10}[/tex]
[tex]y=20[/tex]
Upon substituting value of y in measure of angle M, we will get:
[tex]m\angle M=6y-10[/tex]
[tex]m\angle M=6(20)-10[/tex]
[tex]m\angle M=120-10[/tex]
[tex]m\angle M=110[/tex]
Therefore, measure of angle M is 110 degrees.
Similarly, we will find the value of angle N as:
[tex]m\angle N=4y-10[/tex]
[tex]m\angle N=4(20)-10[/tex]
[tex]m\angle N=80-10[/tex]
[tex]m\angle N=70[/tex]
Therefore, measure of angle N is 70 degrees.
