Answer:
Explanation:
4) The shape in the figure is a parallelogram. In the parallelogram, the diagonals are equal and bisect each other at the midpoint, E. This means that AC is divided equally into AE and EC. Therefore
AC = 2EC
AC = 8x - 14 and EC = 2x + 11. So,
8x - 14 = 2(2x + 11)
8x - 14 = 4x + 22
8x - 4x = 22 + 14
4x = 36
x = 36/4
x = 9
6)The shape in the figure is a parallelogram. The opposite angles are equal. This means that
Angle BCD = angle BED
So angle BED = 51 degrees.
Since the sum of angles in a triangle is 180 degrees, then, angle BED + angle BDE + angle DBE = 180 degrees. It means
51 + 55 + 14x + 4 = 180
14x + 110 = 180
14x = 180 - 110 = 70
x = 70/14
x = 5
7) The shape in the figure is a parallelogram. The opposite angles are equal. Therefore,
angle VST = angle VUT
5x + 23 = 8x - 49
5x - 8x = -49 - 23
-3x = -72
x = -72 / -3
x = 24
angle VST = 5×24 + 23 = 143
angle VUT = 143
angle VST + angle VUT = 143 + 1143 = 286
Recall, the sum of angles in a parallelogram is 360 degrees. Therefore,
angle SVU + angle STU = 360 - 286 = 74 degrees
Angle SVU = 74/2 = 37 degrees.
Angle SVT + angle UVT = 37
angle SVT + 20 = 37
angle SVT = 37 - 20 = 17 degrees