CDE ~ PQR. mLC = 13°
, mLD = 65"
. What are the measures of
angles P. Q, and R?
To find the measures of angles P, Q, and R, we first need to determine the relationship between angles CDE and PQR.
Since angle CDE corresponds to angle PQR, we know that angle C is corresponding to angle P, angle D is corresponding to angle Q, and angle E is corresponding to angle R.
Given that mLC is 13° and mLD is 65°, we have:
Angle C + Angle D + Angle E = 180° (sum of interior angles of a triangle)
Angle P + Angle Q + Angle R = 180°
Since angle C is corresponding to angle P, angle D is corresponding to angle Q, and angle E is corresponding to angle R, we can set up the following equations:
Angle C = 13°
Angle D = 65°
Angle E = Unknown
Solving for angle E:
Angle C + Angle D + Angle E = 180°
13° + 65° + Angle E = 180°
78° + Angle E = 180°
Angle E = 180° - 78°
Angle E = 102°
Now we can find angles P, Q, and R:
Angle P = 13°
Angle Q = 65°
Angle R = 102°
Therefore, the measures of angles P, Q, and R are 13°, 65°, and 102° respectively.