Question

△PQR is similar to △STU . In addition, m∠U=96° and m∠T=6(m∠P) . What is m∠P ? Enter your answer in the box. °

Answer 1

△PQR is similar to △STU

m∠R = m∠U = 96°

m∠Q = m∠T = 6

m∠P = 180 - ( 96 + 6)

m∠P = 180 - 102

m∠P = 78
 
answer 

m∠P = 78

Answer 2

Answer:

$m\angle P=12^{\circ}$

Step-by-step explanation:

Two triangles are similar if their angles are equal one to one.

So:

$m\angle P= m\angle S\\m\angle Q= m\angle T\\m\angle R= m\angle U$

Also, the problem provided this data:

$m\angle T= 6(m\angle P)$

As you may know, the sum of the interior angles of a triangle is equal to 180, so:

$m\angle S+m\angle T + m\angle U=180\\\\Where:\\\\m\angle T=6(m\angle P)\\\\So:\\\\m\angle S+6(m\angle P) + m\angle U=180$

and:

$m\angle P=m\angle S\\\\Hence\\\\m\angle S+6(m\angle S) + m\angle U=180\\\\7(m\angle S) + m\angle U=180\\\\7(m\angle S) + 96=180$

Solving for $m\angle S$

$m\angle S =\frac{180-96}{7} =12^{\circ}$

Since:

$m\angle P= m\angle S=12^{\circ}$

Therefore $m\angle P=12^{\circ}$