∆CDE~∆PQR m→C =13°, m→D = 65°. What are the measurements of angles P,Q and R.

m→P= blank°
m→Q= blank°
m→R= blank°

1 answer

Since triangles \( \Delta CDE \) and \( \Delta PQR \) are similar (denoted by \( \Delta CDE \sim \Delta PQR \)), their corresponding angles are equal.

Given that:

  • \( m\angle C = 13° \)
  • \( m\angle D = 65° \)

We can find \( m\angle E \) using the fact that the sum of the angles in a triangle is \( 180° \):

\[ m\angle E = 180° - m\angle C - m\angle D \] \[ m\angle E = 180° - 13° - 65° = 102° \]

Now we know the angles of triangle \( CDE \):

  • \( m\angle C = 13° \)
  • \( m\angle D = 65° \)
  • \( m\angle E = 102° \)

Since triangles \( CDE \) and \( PQR \) are similar, we have:

  • \( m\angle P = m\angle C = 13° \)
  • \( m\angle Q = m\angle D = 65° \)
  • \( m\angle R = m\angle E = 102° \)

Thus, the measurements of the angles in triangle \( PQR \) are:

  • \( m\angle P = 13° \)
  • \( m\angle Q = 65° \)
  • \( m\angle R = 102° \)