Answer: No 1; x = 44 and
No 2; YA = 8
Step-by-step explanation: In the first parallelogram ABCD, angle D measures x, while angle A measures 3x + 4. Both angles are on the same side of the parallelogram and that means angles A and C are equal while angles B and D are also equal. It also means angles A and D are supplementary (that is, angle A and angle D equals 180). That being the case,
Angle A + Angle D = 180
3x + 4 + x = 180
4x + 4 = 180
Subtract 4 from both sides of the equation
4x = 176
Divide both sides of the equation by 4
x = 44
In the second parallelogram XYZW, diagonal XZ bisects diagonal YW at point A. Where both diagonals bisect each other, is the midpoint for both lines XZ and YW respectively. Hence, line YA equals line WA which can be expressed as
YA = WA
2t = 3t - 4
By collecting like terms we now have
4 = 3t - 2t
4 = t
If t = 4, then 2t (line YA) equals;
YA = 2t
YA = 2(4)
YA = 8
Therefore, (No 1) x = 44,
(No 2) YA = 8
