Based on parallelogram EFGH shown above, the measures of angle H and side HG are;
m∠H = 45°.
HG = 12 units.
In Mathematics, a parallelogram is a type of quadrilateral and two-dimensional geometrical figure that is composed of two equal and parallel opposite sides.
According to the opposite angles theorem, the opposite angles of a parallelogram are always congruent or equal and as such, we have the following:
3x - 15 + 3x - 15 + 7x - 5 + 7x - 5 = 360
20x - 40 = 360
x = 400/20
x = 20°
For the measure of angle H, we have;
m∠H = 3x - 15
m∠H = 3(20) - 15
m∠H = 45°
For side length HG, we have;
y + 8 = 3y
2y = 8
y = 8/2 = 4
HG = y + 8
HG = 4 + 8
HG = 12 units.