Answer:
[tex]m=60\°[/tex] and [tex]n=30\°[/tex]
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
[tex]x+x+x=180\°[/tex], using the theorem that states that all internal angles in a triangle sum 180°.
Now, solving for [tex]x[/tex], we have
[tex]3x=180\°\\x=\frac{180\°}{3}\\ x=60\°[/tex]
Then, you can observe int he graph that [tex]\angle n[/tex] and one angle of the equilateral triangle are complementary, that is
[tex]x+n=90\°[/tex], and we know that [tex]x=60\°[/tex], so [tex]n[/tex] would be
[tex]60\°+n=90\°\\n=90\°-60\°\\n=30\°[/tex]
We also now that [tex]m+n=90\°[/tex], because they are acute angles of the right triangles, which by theorem they sum 90°, replacing [tex]n[/tex] and solving for [tex]m[/tex], we have
[tex]m+n=90\°\\m+30\°=90\°\\m=90\°-30\°\\m=60\°[/tex]
Therefore, the values are
[tex]m=60\°[/tex] and [tex]n=30\°[/tex]
