△CDE∼△PQR

. m∠C=13°
, m∠D=65°
. What are the measures of angles P, Q, and R?(2 points)
m∠P =

°
, m∠Q =

°
and m∠R=

°

1 answer

Since △CDE is similar to △PQR (denoted as △CDE ∼ △PQR), the corresponding angles of the triangles are equal.

Given:

  • m∠C = 13°
  • m∠D = 65°

To find m∠E, we use the fact that the sum of angles in a triangle is 180°:

\[ m∠E = 180° - m∠C - m∠D \] \[ m∠E = 180° - 13° - 65° \] \[ m∠E = 180° - 78° = 102° \]

Now, we can match the angles of △CDE with △PQR:

  • m∠C = m∠P
  • m∠D = m∠Q
  • m∠E = m∠R

Thus, we have:

  • m∠P = m∠C = 13°
  • m∠Q = m∠D = 65°
  • m∠R = m∠E = 102°

So the measures of the angles in triangle PQR are:

  • m∠P = 13°
  • m∠Q = 65°
  • m∠R = 102°

Final answers:

  • m∠P = 13°
  • m∠Q = 65°
  • m∠R = 102°