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

`m=60\°` and
`n=30\°`

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=(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\°`