Answer:
[tex]m\angle P=12^{\circ}[/tex]
Step-by-step explanation:
Two triangles are similar if their angles are equal one to one.
So:
[tex]m\angle P= m\angle S\\m\angle Q= m\angle T\\m\angle R= m\angle U[/tex]
Also, the problem provided this data:
[tex]m\angle T= 6(m\angle P)[/tex]
As you may know, the sum of the interior angles of a triangle is equal to 180, so:
[tex]m\angle S+m\angle T + m\angle U=180\\\\Where:\\\\m\angle T=6(m\angle P)\\\\So:\\\\m\angle S+6(m\angle P) + m\angle U=180[/tex]
and:
[tex]m\angle P=m\angle S\\\\Hence\\\\m\angle S+6(m\angle S) + m\angle U=180\\\\7(m\angle S) + m\angle U=180\\\\7(m\angle S) + 96=180[/tex]
Solving for [tex]m\angle S[/tex]
[tex]m\angle S =\frac{180-96}{7} =12^{\circ}[/tex]
Since:
[tex]m\angle P= m\angle S=12^{\circ}[/tex]
Therefore [tex]m\angle P=12^{\circ}[/tex]
