Question

Find the measures of angels of M and NM (6y-10)N (4y-10)

Answer 1

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:

$\angle M+\angle N=180$

$(6y-10)+(4y-10)=180$  

$6y-10+4y-10=180$

$10y-20=180$

$10y-20+20=180+20$

$10y=200$

$\frac{10y}{10}=\frac{200}{10}$

$y=20$

Upon substituting value of y in measure of angle M, we will get:

$m\angle M=6y-10$

$m\angle M=6(20)-10$

$m\angle M=120-10$

$m\angle M=110$

Therefore, measure of angle M is 110 degrees.

Similarly, we will find the value of angle N as:

$m\angle N=4y-10$

$m\angle N=4(20)-10$

$m\angle N=80-10$

$m\angle N=70$

Therefore, measure of angle N is 70 degrees.