Question

Find the values of m and n

Answer 1

M would be 90 degrees and n would most likely be 15 (it will be less than 90 for sure since it's an acute angle but what are your options?)

Answer 2

Answer:

$m=60\°$ and $n=30\°$

Step-by-step explanation:

In the graph we have two triangle, an equilateral and a right triangle.

By definition, an equilateral triangle has all sides equal. Additionally, there's a theorem which states that all internal angles of a equilateral triangle are the same, which means

$x+x+x=180\°$, using the theorem that states that all internal angles in a triangle sum 180°.

Now, solving for $x$, we have

$3x=180\°\\x=\frac{180\°}{3}\\ x=60\°$

Then, you can observe int he graph that $\angle n$ and one angle of the equilateral triangle are complementary, that is

$x+n=90\°$, and we know that $x=60\°$, so $n$ would be

$60\°+n=90\°\\n=90\°-60\°\\n=30\°$

We also now that $m+n=90\°$, because they are acute angles of the right triangles, which by theorem they sum 90°, replacing $n$ and solving for $m$, we have

$m+n=90\°\\m+30\°=90\°\\m=90\°-30\°\\m=60\°$

Therefore, the values are

$m=60\°$ and $n=30\°$