Answer:
m<PQR = 82°
Step-by-step explanation:
In a Rhombus, the diagonals bisect its angles. This means that they divide each the four angles into two equal parts.
Therefore:
(4x - 27)° = (2x + 7)°
Solve for x
4x - 27 = 2x + 7
Collect like terms
4x - 2x = 27 + 7
2x = 34
Divide both sides by 2
2x/2 = 34/2
x = 17
✔️m<PQR = (4x - 27) + (2x + 7)
Plug in the value of x
m<PQR = (4*17 - 27) + (2*17 + 7)
m<PQR = 41 + 41
m<PQR = 82°
