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

`m\angle P=12^(\circ)`

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 =(180-96)/(7) =12^(\circ)`

Since:

`m\angle P= m\angle S=12^(\circ)`

Therefore
`m\angle P=12^(\circ)`