Question

find the values of m and nthe value of m is....°the value of n is.....°

Answer 1

From the figure:

we can see that angles q and 130 are supplementary. This imply

$\begin{gathered} q+130=180 \\ q=180-130 \\ q=50 \end{gathered}$

Then, we can draw the following picture:

since interior angles of a triangle adds up to 180, we have

$\begin{gathered} 90+50+m=180 \\ 140+m=180 \\ m=180-140 \\ m=40 \end{gathered}$

Now we have the following picture:

so, this correspond to an isosceles triangles because the side AB is equal to the side AC. Then, angles at C and B are the same. This imply that:

$\begin{gathered} 130+n+n=180 \\ 130+2n=180 \\ 2n=180-130 \\ 2n=50 \\ n=\frac{50}{2} \\ n=25 \end{gathered}$

Therefore, the answer is m=40 and n=25