triangleCDE ~trianglePQR

Question

m<C=20 degrees
m<D= 60 degrees
what are the measures of angles P,Q,and R?

Answer 1

Since triangle CDE is similar to triangle PQR (indicated by the notation triangleCDE ~ trianglePQR), the corresponding angles are equal.

We know the measures of angles C and D:

• \( m\angle C = 20^\circ \)
• \( m\angle D = 60^\circ \)

To find the measure of angle E in triangle CDE, we use the fact that the sum of the angles in any triangle is \(180^\circ\): \[ m\angle E = 180^\circ - m\angle C - m\angle D \] \[ m\angle E = 180^\circ - 20^\circ - 60^\circ \] \[ m\angle E = 100^\circ \]

Now we have all the angles in triangle CDE:

• \( m\angle C = 20^\circ \)
• \( m\angle D = 60^\circ \)
• \( m\angle E = 100^\circ \)

In triangle PQR, the corresponding angles are:

• \( m\angle P = m\angle C = 20^\circ \)
• \( m\angle Q = m\angle D = 60^\circ \)
• \( m\angle R = m\angle E = 100^\circ \)

Thus, the measures of the angles in triangle PQR are:

• \( m\angle P = 20^\circ \)
• \( m\angle Q = 60^\circ \)
• \( m\angle R = 100^\circ \)