Triangle CDE ~ Triangle PQR,M<C =13*, m<D = 65 degrees what are the measures of angles P, Q and R
Since triangles CDE and PQR are similar, the corresponding angles must be equal.
Given that m<C = 13°, m<D = 65°, we can determine two corresponding angles in triangle PQR.
Since ∠CDE is corresponding to ∠PQR, m<PQR = m<CDE = 13°.
Similarly, ∠DCE is corresponding to ∠PQR, so m<PQR = m<DCE = 65°.
Therefore, the measures of angles P, Q, and R are:
∠P = ∠CDE = 13°,
∠Q = ∠DCE = 65°,
∠R = ∠ECD = ∠EDC.
To determine the measure of ∠R, we can use the fact that the sum of the angles in a triangle is 180°.
∠CDE + ∠DCE + ∠ECD = 180°
13° + 65° + ∠R = 180°
78° + ∠R = 180°
∠R = 180° -78°
∠R = 102°
Therefore, the measures of angles P, Q, and R are:
∠P = 13°
∠Q = 65°
∠R = 102°