To find the measures of angles P, Q, and R, we need to determine their respective values using the given information.
We are given that m<C = 13 and m<D = 65.
Looking at triangle CDE, angle C and angle D are two of its interior angles. Since the sum of all interior angles of a triangle is 180 degrees, we can write the equation:
m<C + m<D + m<E = 180
Substituting the given values, we have:
13 + 65 + m<E = 180
78 + m<E = 180
m<E = 180 - 78
m<E = 102
Now, let's consider triangle PQR. Angle CDE (or angle E) is one of its interior angles. Since the sum of all interior angles of a triangle is 180 degrees, we can write the equation:
m<P + m<Q + m<R + m<E = 180
Substituting the given values, we have:
m<P + m<Q + m<R + 102 = 180
m<P + m<Q + m<R = 180 - 102
m<P + m<Q + m<R = 78
Therefore, the measures of angles P, Q, and R are as follows:
m<P = angle P
m<Q = angle Q
m<R = angle R
m<P + m<Q + m<R = 78