Answer
Angle PQR = 82°
Step-by-step explanation
Tosolve this, we just need to note one thing about the properties of a rhombus;
The diagonals of a rhombus bisects its angles into two equal parts.
So, this means that
4x - 27° = 2x + 7°
4x - 2x = 27° + 7°
2x = 34°
Divide both sides by 2
(2x/2) = (34°/2)
x = 17°
We are then asked to solve for Angle PQR
Angle PQR = 4x - 27° + 2x + 7°
Angle PQR = 6x - 20°
Recall that x = 17°
Angle PQR = 6x - 20°
Angle PQR = 6(17°) - 20°
Angle PQR = 102° - 20°
Angle PQR = 82°
Hope this Helps!!!