Question

In fig 5.26, $\square$WXYZ is a parallelogram, find the values of x and y.

Answer 1

Because $\square$WXYZ is a parallelogram, side WZ || side XY and seg XZ is a transversal.
Thus, we have:
$\angle$WZX = $\angle$ZXY [Alternate angles]
Also,
$\angle$WZX = 28° and $\angle$ZXY = 4y
∴ 4y = 28°
$\Rightarrow$y = 7°
Since $\square$WXYZ is a parallelogram, side WX || side YZ and seg XZ is a transversal.
Thus, we have:
$\angle$WXZ = $\angle$YZX [Alternate angles]
Also,
$\angle$WXZ = 10x and $\angle$YZX = 60°
Thus, we have:
10x = 60°
$\Rightarrow$x = 6°
Thus, we get:
x = 6° and y = 7°